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Following our previous study of the Bohr–Sommerfeld (BS) quantization condition for one-dimensional case [J. C. del Valle and A. V. Turbiner, Int. J. Mod. Phys. A36, 2150221 (2021)], we extend it to d -dimensional power-like radial potentials. The BS quantization condition for S -states of the d -dimensional radial Schrödinger equation is proposed. Based on numerical results obtained for the spectra of power-like potentials, V (r) = r m with m ∈ [ − 1 , ∞) , the correctness of the proposed BS quantization condition is established for various dimensions d. It is demonstrated that by introducing the WKB correction γ into the right-hand side of the BS quantization condition leads to the so-called exact WKB quantization condition, which reproduces the exact energies, while γ remains always very small. For m = 2 (any integer d) and for m = − 1 (at d = 2) the WKB correction γ = 0 : for S states the BS spectra coincides with the exact ones. Concrete calculations for physically important cases of linear, cubic, quartic and sextic oscillators, as well as Coulomb and logarithmic potentials in dimensions d = 2 , 3 , 6 are presented. Radial quartic anharmonic oscillator is considered briefly. [ABSTRACT FROM AUTHOR]

The problem of time in the quantization of gravity arises from the fact that time in Schrödinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time" in QM and "time" in general relativity (GR) are seen as mutually incompatible notions. The introduction of a dynamical time operator in relativistic quantum mechanics (RQM), that follows from the canonical quantization of special relativity and that in the Heisenberg picture is also a function of the parameter t (identified as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of time in the canonical quantization approach to quantum gravity is developed. [ABSTRACT FROM AUTHOR]

In this paper, one of the most important diagrams of weak interaction (vacuum polarization) is studied in Krein space quantization (KSQ). This diagram has divergent terms in Hilbert space which must be eliminated using a traditional regularization method like dimensional regularization whereas in KSQ the result is automatically finite and does not need renormalization. [ABSTRACT FROM AUTHOR]

The functional Schrödinger representation of a scalar field on an n -dimensional static space-time background is argued to be a singular limiting case of the hypercomplex quantum theory of the same system obtained by the precanonical quantization based on the space-time symmetric De Donder–Weyl Hamiltonian theory. The functional Schrödinger representation emerges from the precanonical quantization when the ultraviolet parameter ϰ introduced by precanonical quantization is replaced by γ ̲ 0 δ inv (0) , where γ ̲ 0 is the time-like tangent space Dirac matrix and δ inv (0) is an invariant spatial (n − 1) -dimensional Dirac's delta function whose regularized value at x = 0 is identified with the cutoff of the volume of the momentum space. In this limiting case, the Schrödinger wave functional is expressed as the trace of the product integral of Clifford-algebra-valued precanonical wave functions restricted to a certain field configuration and the canonical functional derivative Schrödinger equation is derived from the manifestly covariant Dirac-like precanonical Schrödinger equation which is independent of a choice of a codimension-one foliation. [ABSTRACT FROM AUTHOR]

We review the basic principles of Quantum Field Theory (QFT) in a brief but comprehensive introduction to the foundations of QFT. The principles of QFT are introduced in canonical and covariant formalisms. The problem of ultraviolet (UV) divergences and its renormalization is analyzed in the canonical formalism. As an application, we review the roots of Casimir effect. For simplicity, we focus on the scalar field theory but the generalization for fermion fields is straightforward. However, the quantization of gauge fields require extra techniques which are beyond the scope of this paper. The special cases of free field theories and conformal invariant theories in lower space-time dimensions illustrate the relevance of the foundations of the theory. Finally, a short introduction to functional integrals and perturbation theory in the Euclidean formalism is included in the last section. [ABSTRACT FROM AUTHOR]

We examine the recently introduced idea of Spin-Field Correspondence (SFC) focusing on the example of the spin system described by the XXZ Heisenberg model with external magnetic field. The Hamiltonian of the resulting nonlinear scalar field theory is derived for arbitrary value of the anisotropy parameter Δ. We show that the linear scalar field theory is reconstructed in the large spin limit. For Δ = 1 , a nonrelativistic scalar field theory satisfying the Born reciprocity principle is recovered. As expected, for the vanishing anisotropy parameter Δ → 0 , the standard relativistic Klein–Gordon field is obtained. Various aspects of the obtained class of the scalar fields are studied, including the fate of the relativistic symmetries and the properties of the emerging interaction terms. We show that, in a certain limit, the so-called polymer quantization of the field variables is recovered. This and other discussed properties suggest a possible relevance of the considered framework in the context of quantum gravity. [ABSTRACT FROM AUTHOR]

In this paper, the fractional singular Lagrangian system is studied. The Hamilton–Jacobi treatment is developed to be applicable for fractional singular Lagrangian system. The equations of motion are obtained for the fractional singular systems and the Hamilton–Jacobi partial differential equations are obtained and solved to determine the action integral. Then the wave function for fractional singular system is obtained. Besides, to demonstrate this theory, the fractional Christ-Lee model is discussed and quantized using the WKB approximation. [ABSTRACT FROM AUTHOR]

In this paper, we study the interaction of quantized radio-frequency (rf)/microwave-field with nuclear spin in Nuclear Magnetic Resonance (NMR) or electron spin in Electron Paramagnetic Resonance (EPR). In magnetic resonance experiments, interaction of quantized rf-field leads to entanglement of spin with the electromagnetic field. In an entangled state, the spins are depolarized with no net transverse magnetization, which cannot give a detectable signal in inductive detection (or Q detection) that detects transverse magnetization. We show that when the electromagnetic field is in coherent state, inductive detection becomes possible. We use the mathematics of quantum optics to study the evolution of a coherent rf-field with a sample of all polarized spins. We show that evolution can be solved in closed form as a separable state of rf-field and spin ensemble, where spin ensemble evolves according to Bloch equations in an rf-field. We extend the analysis and results to a spin ensemble with Boltzmann polarization. The rabi frequency and coupling strength of spins to rf-field depends on number state of the rf-field. We show that in interaction with a coherent rf-field, this variation in coupling strength introduces negligible error. [ABSTRACT FROM AUTHOR]

The quantization of the electrical charge in the electrodynamics and of the hypercharge in the standard model are imposed in the theory based not on theoretical arguments but on the experimental observations. In this paper we propose a quantum consistency condition in a theory where Ward identities are respected that requires the quantization of the charge within the framework of the theory without external impositions. This refers to the renormalization conditions in the background gauge field method such that to ensure a correct mathematical correspondence between the bare partition function and the renormalized one. Applied to the standard model of elementary particles our criterion together with the anomaly cancellation condition leads to the correct hypercharge assignment of all standard model fermions. [ABSTRACT FROM AUTHOR]

A noncommutative negative order AKNS (NC-AKNS(-1)) equation is studied. To show the integrability of the system, we present explicitly the underlying integrable structure such as Lax pair, zero-curvature condition, an infinite sequence of conserved densities, Darboux transformation (DT) and quasideterminant soliton solutions. Moreover, the NC-AKNS(-1) equation is compared with its commutative counterpart not only on the level of nonlinear evolution equation but also for the explicit solutions. [ABSTRACT FROM AUTHOR]

In this paper, we study a new type of immunization strategy which is applied to weighted networks. It helps us in maintaining the necessary network efficiency by limiting the transmission (lowering the weight of edges) while suppressing the spread of the epidemic. It is similar to the inflammation around the infected parts of our body, which can not only prevent the disease spreading but also protect the function of the body. First, we set the rate of transmission to be proportional to the edge weight based on the S-I epidemic spreading model. Then, we show the detailed dynamic evolution of the infected nodes which facilitates an effective epidemic control. Theoretical analysis and simulation results indicate that the new immunization strategy can be used to prevent the epidemic spreading effectively, while maintaining the high efficiency of the network. [ABSTRACT FROM AUTHOR]

A quantum model for the interaction between asymmetric two two-level atoms and an electromagnetic field is presented. The k -photon processes and atom–atom interaction are considered in this quantum model. The wavefunction for asymmetric case of the proposed model is obtained analytically. While, the explicit analytical formula of the wavefunction for symmetric case was calculated in previous works. Initially, the electromagnetic field is in the coherent state and two two-level atoms are identical in the excited states. For the proposed model, some statistical aspects are obtained, such as the linear entropy, atomic population inversion, entropy squeezing, atomic variance and von Neumann entropy. The evaluations of these statistical properties are discussed for the variation in the detuning parameters. Moreover, the nonclassical effects for atom–atom interaction are observed. [ABSTRACT FROM AUTHOR]

In this paper we study the quantization of a massless scalar field in a rotating frame. In particular, we obtain the Casimir energy in a space–time with one extra compactified dimension for a rotating observer. We consider a uniformly rotating system on the circle S1 and present an equation for spin-0 bosons where noninertial effects can be taken into account. It is shown that the spectrum of the scalar field depends on the angular velocity of the rotating system and in this way, positive and negative modes can be defined through an appropriate choice of the angular velocity. We show that noninertial effects restrict the physical region of the space–time where particles can be placed, and furthermore that the Casimir energy in the space–time with one extra compactified dimension is shifted by these effects. In addition, we pointed out that rotating effects modify the length of the extra dimension for a co-rotating observer in this kind of space–time. [ABSTRACT FROM AUTHOR]

Light-front (LF) quantization of massless fields in two spacetime dimensions is a long-standing and much debated problem. Even though the classical wave-equation is well-documented for almost two centuries, either as problems with initial values in spacetime variables or with initial data on characteristics in light-cone variables, the way to a consistent quantization in both types of frames is still a puzzle in many respects. This is in contrast to the most successful Conformal Field Theoretic (CFT) approach in terms of complex variables z , z ̄ pioneered by Belavin, Polyakov and Zamolodchikov in the ’80s. It is shown here that the 2D-massless canonical quantization in both reference frames is completely consistent provided that quantum fields are treated as Operator-Valued Distributions (OPVD) with Partition of Unity (PU) test functions. We recall first that classical fields have to be considered as distributions (e.g. generalized functions in the Russian literature). Then, a necessary condition on the PU test function follows from the required matching of the classical solutions of the massless differential equations in both types of reference frame. Next we use a mathematical formulation for OPVD, developed in the recent past. Specifically, smooth 𝒞 ∞ fields are introduced through the convolution operation in the distributional context. Due to the specific behavior of the Fourier-transform of the initial test function, this convolution transform has a well-defined integral in the dual space, whatever the initial choice of the reference frame. The relation to the conformal fields method follows immediately from the transition to Euclidean time and leads directly to explicit calculations of a few correlation functions of the scalar field and its energy–momentum tensor. The LF derivation of the Virasoro algebra is then obtained from the z and z ̄ expansions of the canonical fields as distributional Laplace-transform in these variables. Finally, the popular and problematic Discretized Light Cone Quantization (DLCQ) method is scrutinized with respect to its zero mode and ultraviolet content as encompassed in the continuum OPVD formulation. [ABSTRACT FROM AUTHOR]

In this paper, we outline the construction of semiclassical eigenfunctions of integrable models in terms of the semiclassical path integral for the Poisson sigma model with the target space being the phase space of the integrable system. The semiclassical path integral is defined as a formal power series with coefficients being Feynman diagrams. We also argue that in a similar way one can obtain irreducible semiclassical representations of Kontsevich’s star product. Dedicated to the memory of L. D. Faddeev [ABSTRACT FROM AUTHOR]

About 30 years ago, in a joint work with L. Faddeev we introduced a geometric action on coadjoint orbits. This action, in particular, gives rise to a path integral formula for characters of the corresponding group G. In this paper, we revisit this topic and observe that the geometric action is a 1-cocycle for the loop group LG. In the case of G being a central extension, we construct Wess–Zumino (WZ) type terms and show that the cocycle property of the geometric action gives rise to a Polyakov–Wiegmann (PW) formula with boundary term given by the 2-cocycle which defines the central extension. In particular, we obtain a PW type formula for Polyakov’s gravitational WZ action. After quantization, this formula leads to an interesting bulk-boundary decoupling phenomenon previously observed in the WZW model. We explain that this decoupling is a general feature of the Wess–Zumino terms obtained from geometric actions, and that in this case, the path integral is expressed in terms of the 2-cocycle which defines the central extension. In memory of our teacher Ludwig Faddeev [ABSTRACT FROM AUTHOR]

We found that quantization of the scanning tunneling microscope (STM) current becomes apparent as the size of a quantum corral (QC) decreases and the corral thickness increases. It is shown that STM current images provide the position dependence of the conduction channels and local density of states (LDOS) images provide the spatial distribution of differential conductance channels. We clarified for the first time that there exist fractal structures in the QC size dependence of the - characteristic and in that of the LDOS. LDOS images also exhibit a fractal structure as a function of bias voltage. These results demonstrate fractal structures in energy space and real space. For an extremely large QC, we found that the - curve becomes Ohmic and the LDOS converges to a constant corresponding to the bulk two-dimensional density of states. [ABSTRACT FROM AUTHOR]

A fully canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric slab is demonstrated. The electric and the magnetic polarization densities of the magneto-dielectric slab are defined in terms of the dynamical variables modeling the slab and the coupling tensors that couple the electromagnetic field to the slab. The four susceptibility tensors of the bi-anisotropic magneto-dielectric slab are expressed in terms of the coupling tensors that couple an electromagnetic field to the slab. It is shown that the four susceptibility tensors of the bi-anisotropic magneto-dielectric slab satisfy Kramers-Kronig relations. The Maxwell's equations are exactly solved in the presence of the bi-anisotropic magneto-dielectric slab. The tangential and the normal components of the Casimir forces exerted on the bi-anisotropic magnet-dielectric slab exactly are calculated in the vacuum state and thermal state of the total system. It is shown that the tangential components of the Casimir forces vanish when the bi-anisotropic slab is converted to an isotropic slab. [ABSTRACT FROM AUTHOR]

In this paper, using the new type of D-dimensional nonperturbative Generalized Uncertainty Principle (GUP) which has predicted both a minimal length uncertainty and a maximal observable momentum,1 first, we obtain the maximally localized states and express their connections to [P. Pedram, Phys. Lett. B 714, 317 (2012)]. Then, in the context of our proposed GUP and using the generalized Schrödinger equation, we solve some important problems including particle in a box and one-dimensional hydrogen atom. Next, implying modified Bohr-Sommerfeld quantization, we obtain energy spectra of quantum harmonic oscillator and quantum bouncer. Finally, as an example, we investigate some statistical properties of a free particle, including partition function and internal energy, in the presence of the mentioned GUP. [ABSTRACT FROM AUTHOR]

We show that our recent Bohr-like approach to black hole (BH) quantum physics implies that spacetime quantization could be energy-dependent. Thus, in a certain sense, spacetime can be neither discrete nor continuous. Our approach also permits to show that the 'volume quantum' of the Schwarzschild spacetime increases with increasing energy during BH evaporation and arrives at a maximum value when the Planck scale is reached and the generalized uncertainty principle (GUP) prevents the total BH evaporation. Remarkably, this result does not depend on the BH original mass. The interesting consequence is that the behavior of BH evaporation should be the same for all Schwarzschild BHs when the Planck scale is approached. [ABSTRACT FROM AUTHOR]

The Wheeler-DeWitt equation was proposed 50 years ago and until now it is the cornerstone of most approaches to quantization of gravity. One can find in the literature, the opinion that the Wheeler-DeWitt equation is even more fundamental than the basic equation of quantum theory, the Schrödinger equation. We still should remember that we are in the situation when no observational data can confirm or reject the fundamental status of the Wheeler-DeWitt equation, so we can give just indirect arguments in favor of or against it, grounded on mathematical consistency and physical relevance. I shall present the analysis of the situation and comparison of the standard Wheeler-DeWitt approach with the extended phase space approach to quantization of gravity. In my analysis, I suppose, first, that a future quantum theory of gravity must be applicable to all phenomena from the early universe to quantum effects in strong gravitational fields, in the latter case, the state of the observer (the choice of a reference frame) may appear to be significant. Second, I suppose that the equation for the wave function of the universe must not be postulated but derived by means of a mathematically consistent procedure, which exists in path integral quantization. When applying this procedure to any gravitating system, one should take into account features of gravity, namely, nontrivial spacetime topology and possible absence of asymptotic states. The Schrödinger equation has been derived early for cosmological models with a finite number of degrees of freedom, and just recently it has been found for the spherically symmetric model which is a simplest model with an infinite number of degrees of freedom. The structure of the Schrödinger equation and its general solution appears to be very similar in these cases. The obtained results give grounds to say that the Schrödinger equation retains its fundamental meaning in constructing quantum theory of gravity. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects. [ABSTRACT FROM AUTHOR]

Fractal self-similarity of hadron interactions demonstrated by the -scaling of inclusive spectra is studied. The scaling regularity reflects fractal structure of the colliding hadrons (or nuclei) and takes into account general features of fragmentation processes expressed by fractal dimensions. The self-similarity variable is a function of the momentum fractions and of the colliding objects carried by the interacting hadron constituents and depends on the momentum fractions and of the scattered and recoil constituents carried by the inclusive particle and its recoil counterpart, respectively. Based on entropy principle, new properties of the -scaling concept are found. They are conservation of fractal cumulativity in hadron interactions and quantization of fractal dimensions characterizing hadron structure and fragmentation processes at a constituent level. [ABSTRACT FROM AUTHOR]

We study the Dirac and the chargeless Klein–Gordon–Fock equations in the geometry of Grumiller’s spacetime that describes a model for gravity of a central object at large distances. The Dirac equation is separated into radial and angular equations by adopting the Newman–Penrose formalism. The angular part of the both wave equations are analytically solved. For the radial equations, we managed to reduce them to one dimensional Schrödinger-type wave equations with their corresponding effective potentials. Fermions’s potentials are numerically analyzed by serving their some characteristic plots. We also compute the quasinormal frequencies of the chargeless and massive scalar waves. With the aid of those quasinormal frequencies, Bekenstein’s area conjecture is tested for the Grumiller black hole. Thus, the effects of the Rindler acceleration on the waves of fermions and scalars are thoroughly analyzed. [ABSTRACT FROM AUTHOR]

We consider the field equations for a flat FRW cosmological model, given by Eq. (??), in an a priori generic gravity model and cast them into a, completely normalized and dimensionless, system of ODEs for the scale factor and the function , with respect to the scalar curvature . It is shown that under reasonable assumptions, namely for power-law functional form for the gravity model, one can produce simple analytical and numerical solutions describing bouncing cosmological models where in addition there are late-time accelerating. The power-law form for the gravity model is typically considered in the literature as the most concrete, reasonable, practical and viable assumption [see S. D. Odintsov and V. K. Oikonomou, Phys. Rev. D 90 (2014) 124083, arXiv:1410.8183 [gr-qc]]. However even without assuming a power-law form for the gravity model, the formulation of the field equations, that is suggested in this paper, is according to the author's viewpoint quite generic in order to analyze the resulting field equations, without any further assumptions. Possibility of extending these results is briefly discussed. [ABSTRACT FROM AUTHOR]

We investigate the theory of an open parafermionic string between two parallel D p-, D q-branes in Ramond and Neveu-Schwarz sectors. Trilinear commutation relations between the string variables are postulated and the corresponding ones in terms of modes are derived. The analysis of the spectrum shows that one can again have a free tachyon Neveu-Schwarz model for some values of the order of the paraquantization associated to some values of p and q. The consistency of this model requires the calculation of the partition function and its confrontation with the results of the degeneracies. A perfect agreement between the two results is obtained and the closure of the Virasoro superalgebra is confirmed. [ABSTRACT FROM AUTHOR]

We discuss the algebraic quantization of a real, massive scalar field in the Poincaré patch of the -dimensional anti-de Sitter spacetime, with arbitrary boundary conditions. By using the functional formalism, we show that it is always possible to associate to such system an algebra of observables enjoying the standard properties of causality, time-slice axiom and F-locality. In addition, we characterize the wavefront set of the ground state associated to the system under investigation. As a consequence, we are able to generalize the definition of Hadamard states and construct a global algebra of Wick polynomials. [ABSTRACT FROM AUTHOR]

We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier-Douady class is torsion. Analogously to usual prequantization, this 2-Hilbert space has the category of sections of the line bundle gerbe as its underlying 2-vector space. These sections are obtained as certain morphism categories in Waldorf's version of the 2-category of line bundle gerbes. We show that these morphism categories carry a monoidal structure under which they are semisimple and abelian. We introduce a dual functor on the sections, which yields a closed structure on the morphisms between bundle gerbes and turns the category of sections into a 2-Hilbert space. We discuss how these 2-Hilbert spaces fit various expectations from higher prequantization. We then extend the transgression functor to the full 2-category of bundle gerbes and demonstrate its compatibility with the additional structures introduced. We discuss various aspects of Kostant-Souriau prequantization in this setting, including its dimensional reduction to ordinary prequantization. [ABSTRACT FROM AUTHOR]

A canonical relativistic quantization of the electromagnetic field is introduced in the presence of an anisotropic conductor magneto-dielectric medium in a standard way in the Gupta-Bleuler framework. The medium is modeled by a continuum collection of the vector fields and a continuum collection of the antisymmetric tensor fields of the second rank in Minkowski space-time. The collection of vector fields describes the conductivity property of the medium and the collection of antisymmetric tensor fields describes the polarization and the magnetization properties of the medium. The conservation law of the total electric charges, induced in the anisotropic conductor magneto-dielectric medium, is deduced using the antisymmetry conditions imposed on the coupling tensors that couple the electromagnetic field to the medium. Two relativistic covariant constitutive relations for the anisotropic conductor magneto-dielectric medium are obtained. The constitutive relations relate the antisymmetric electric-magnetic polarization tensor field of the medium and the free electric current density four-vector, induced in the medium, to the strength tensor of the electromagnetic field, separately. It is shown that for a homogeneous anisotropic medium the susceptibility tensor of the medium satisfies the Kramers-Kronig relations. Also it is shown that for a homogeneous anisotropic medium the real and imaginary parts of the conductivity tensor of the medium satisfy the Kramers-Kronig relations and a relation other than the Kramers-Kronig relations. [ABSTRACT FROM AUTHOR]

We employ here the enhancement of the vector potential amplitude quantization at a single photon state. The analysis of the general solution of the vector potential, obtained by resolving Maxwell's equations, implies that the amplitude is proportional to the angular frequency. The photon vector potential function αkλ(r, t) can be written in the plane wave representation satisfying the classical wave propagation equation, Schrödinger's equation for the energy with the relativistic massless field Hamiltonian and a linear time-dependent equation for the vector potential amplitude operator. Thus, the vector potential αkλ(r, t) with the quantized amplitude may play the role of a real wave function for the photon in a nonlocal representation that can be suitably normalized. We then deduce that the amplitudes of the electric and magnetic fields, respectively, of a single free photon are proportional to the square of the angular frequency. This might open perspectives for the development of nondestructive photon detection methods based on the influence of the electric and/or magnetic fields of photons on the energy levels of atoms and molecules. [ABSTRACT FROM AUTHOR]

The proper-time regularization of bosonic string reproduces the results of canonical quantization in a special scaling limit where the length in target space has to be renormalized. We repeat the analysis for the Pauli-Villars regularization and demonstrate the universality of the results. In the mean-field approximation, we compute the susceptibility anomalous dimension and show it equals 1/2. We discuss the relation with the previously known results on lattice strings. [ABSTRACT FROM AUTHOR]

In the canonical approach to quantization of gravity, one often uses relational clock variables and an interpretation in terms of conditional probabilities to overcome the problem of time. In this essay, we show that these suffer from serious conceptual issues. [ABSTRACT FROM AUTHOR]

A major issue that has challenged physics is the goal of bringing gravity into a complete unification of the interactions and the quantization of gravity. We build upon the appreciation that electromagnetic waves are also gravitational waves because they transport local spacetime curvature. Logical steps lead us to appreciate the totality of the traditional quantized particles in nature as gravitational quanta. Thus, our present particle physics model is seen to be unified with the gravitational interaction. Whether there remains a scope for the existence of a spin-2 graviton in vacuum is brought into question by our invariant energy construct centered upon the Ricci tensor. We suggest that this construct holds the key to ultra-strong gravity's essential role in quantization. [ABSTRACT FROM AUTHOR]

In the study of covariant wave equations, linear gravity manifests itself through the metric deviation and a two-point vector potential itself constructed from and its derivatives. The simultaneous presence of the two gravitational potentials is noncontradictory. Particles also assume the character of quasiparticles and carries information about the matter with which it interacts. We consider the influence of on the dispersion relations of the particles involved, the particles' motion, quantum tunneling through a horizon, radiation, energy-momentum dissipation and flux quantization. [ABSTRACT FROM AUTHOR]

The spectrum of masses of the colorless states of DW Hamiltonian operator of quantum SU(2) Yang-Mills field theory on obtained via the precanonical quantization is shown to be purely discrete and bounded from below. The scale of the mass gap is estimated to be of the order of magnitude of the scale of the ultra-violet parameter which is introduced by precanonical quantization on dimensional grounds. [ABSTRACT FROM AUTHOR]

We study the effect of Freudenthal duality on supersymmetric extremal black hole attractors in , ungauged supergravity. Freudenthal duality acts on the dyonic black hole charges as an anti-involution which keeps the black hole entropy and the critical points of the effective black hole potential invariant. We analyze its effect on the recently discovered distinct, mutually exclusive phases of axionic supersymmetric black holes, related to the existence of nontrivial involutory constant matrices. In particular, we consider a supersymmetric black hole and we explicitly Freudenthal-map it to a supersymmetric black hole. We thus show that the charge representation space of a supersymmetric black hole also contains mutually exclusive domains. [ABSTRACT FROM AUTHOR]

The quantization scheme based on reduction of the physical states I. Y. Park, Hypersurface foliation approach to renormalization of ADM formulation of gravity, Eur. Phys. J. C 75(9) (2015) 459, arXiv:1404.5066 [hep-th] is extended to two gravity-matter systems and pure de Sitter (dS) gravity. For the gravity-matter systems, we focus on quantization in a flat background for simplicity, and renormalizability is established through gauge-fixing of matter degrees of freedom. Quantization of pure dS gravity has several new novel features. It is noted that the infrared divergence does not arise in the present scheme of quantization. The lapse function constraint plays a crucial role. [ABSTRACT FROM AUTHOR]

Hořava's quantum gravity at a Lifshitz point is a theory intended to quantize gravity by using traditional quantum field theories. To avoid Ostrogradsky's ghosts, a problem that has been facing in quantization of general relativity since the middle of 1970's, Hořava chose to break the Lorentz invariance by a Lifshitz-type of anisotropic scaling between space and time at the ultra-high energy, while recovering (approximately) the invariance at low energies. With the stringent observational constraints and self-consistency, it turns out that this is not an easy task, and various modifications have been proposed, since the first incarnation of the theory in 2009. In this review, we shall provide a progress report on the recent development of Hořava gravity. In particular, we first present four so far most-studied versions of Hořava gravity, by focusing first on their self-consistency and then their consistency with experiments, including the solar system tests and cosmological observations. Then, we provide a general review on the recent development of the theory in three different but also related areas: (i) universal horizons, black holes and their thermodynamics, (ii) nonrelativistic gauge/gravity duality and (iii) quantization of the theory. The studies in these areas can be easily generalized to other gravitational theories with broken Lorentz invariance. [ABSTRACT FROM AUTHOR]

By proceeding with the idea that the presence of physical (BRST invariant) extra factors in the path integral is equivalent to taking into account explicitly the arbitrariness in resolving the quantum master equation, we consider the field-antifield quantization procedure both with the Abelian and the non-Abelian gauge fixing. [ABSTRACT FROM AUTHOR]

Quantum computers by their nature are many particle quantum systems. Both the many-particle arrangement and being quantum are necessary for the existence of the entangled states, which are responsible for the parallelism of the quantum computers. Second quantization is a very important approximate method of describing such systems. This lecture will present the general idea of the second quantization, and discuss shortly some of the most important formulations of second quantization. [ABSTRACT FROM AUTHOR]

We propose a topological model of induced gravity (pregeometry) where both Newton's coupling constant and the cosmological constant appear as integration constants in solving field equations. The matter sector of a scalar field is also considered, and by solving field equations it is shown that various types of cosmological solutions in the Friedmann-Robertson-Walker (FRW) universe can be obtained. A detailed analysis is given of the meaning of the BRST transformations, which make the induced gravity be a topological field theory, by means of the canonical quantization analysis, and the physical reason why such BRST transformations are needed in the present formalism is clarified. Finally, we propose a dynamical mechanism for fixing the Lagrange multiplier fields by following the Higgs mechanism. The present study clearly indicates that the induced gravity can be constructed at the classical level without recourse to quantum fluctuations of matter and suggests an interesting relationship between the induced gravity and the topological quantum-field theory (TQFT). [ABSTRACT FROM AUTHOR]

Quantum entanglement is discussed as a consequence of the quantization of fields. The inclusion of quantum fields self-consistently explains some quantum paradoxes (EPR and Hardy's paradox). The definition of entanglement was introduced, which depends on the maximum energy of the interaction of particles. The destruction of entanglement is caused by the creation and annihilation of particles. On this basis, an algorithm for quantum particle evolution was formulated. [ABSTRACT FROM AUTHOR]

Energy of a black hole is usually quantized by invoking some area quantization scheme after expressing the energy in terms of the horizon area. However, in this approach one has to quantize the local and asymptotic energy of the black hole separately and the two results do not manifest any physical correspondence with each other. Here, as opposed to this practice, we find the unique energy spectrum of black holes by adopting a top-down approach. The physical links among the underlying quantum theory, statistical mechanics and thermodynamics of the black hole horizon play the central role in determining the energy spectrum. The energy spectrum that we obtain explicitly reveals the correspondence between asymptotic and local observations through the presence of the surface gravity of the horizon as a parameter in the spectrum, rather than being expressed as a function of area and consequently getting quantized in the usual approach. Thus, our result presents a new view as far as black hole energy quantization is concerned. The calculations are performed using the quantum geometric description of black hole horizons as laid down by loop quantum gravity. [ABSTRACT FROM AUTHOR]

This is a tribute to Abdus Salam's memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in spacetime (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time. [ABSTRACT FROM AUTHOR]

We study the evolution of a quantum discrete nonlinear Schrödinger (DNLS) system using as initial conditions coherent states corresponding to points in the vicinity of breather solutions of the classical system. We consider various examples of stable and unstable breathers and examine the distance between exactly evolved states and coherent states with parameters that evolve according to classical dynamics. Initial conditions near stable breathers and their vicinity are seen to lead to recurrences to small distances between the two evolving states. Similar recurrences are not observed for initial conditions near unstable breathers. [ABSTRACT FROM AUTHOR]

Using the Batalin, Fradkin and Tyutin approach, the second-class higher derivative Maxwell-Chern-Simons-Proca model is converted into a mixed constrained one and then, the Hamiltonian path integral of the resulting mixed constrained system is constructed. The Hamiltonian path integral takes a manifestly Lorentz covariant form. [ABSTRACT FROM AUTHOR]

Coherent light propagating in a bulk Kerr nonlinear defocusing medium obeys nonlinear Schrödinger (NLS) equation, which is similar to the Gross-Pitaevskii equation for Bose-Einstein condensates (BECs). An equivalent hydrodynamic approach allows one to consider propagation of light as a flow of an equivalent 'luminous fluid.' An analog optical event horizon can be formed when the flow velocity of this fluid equals the local sound velocity, determined by the nonlinear term in the NLS equation. The analog event horizon is characterized by a finite width, also determined by the nonlinearity length, or by the healing length in Bose-Einstein condensates. The various eigenmodes of fluctuations are found in the immediate vicinity of the event horizon and the scattering matrix due to the finite width horizon is calculated to be within the leading order corrections in the nonlinearity length. The Hawking radiation is found to be enhanced with respect to that of a Planck's black body spectrum and is characterized by the emissivity greater than one. A procedure of paraxial quantization of the fluctuation field is discussed and its connection to the conventional quantization of the electromagnetic field is demonstrated. Quantum fluctuations of the electric field energy and those of its flow are calculated. [ABSTRACT FROM AUTHOR]

We show using simple arguments, that the conceptual triad of a classical black hole, semi-classical Hawking emission and geometry quantization is inherently, mutually incompatible. Presence of any two explicitly violates the third. We argue that geometry quantization, if realized in nature, magnifies the quantum gravity features hugely to catapult them into the realm of observational possibilities. We also explore a quantum route towards extremality of the black holes. [ABSTRACT FROM AUTHOR]