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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 discuss the problems of dynamics of the gravitational field and try to solve them according to quantum field theory by suggesting canonical states for the gravitational field and its conjugate field. To solve the problem of quantization of gravitational field, we assume that the quantum gravitational field eI changes the geometry of curved spacetime xµ, and relate this changing to quantization of the gravitational field. We introduce a field πI and consider it as a canonical momentum conjugates to a canonical gravitational field e-I. We use them in deriving the path integral of the gravitational field according to quantum field theory, we get Lagrangian with dependence only on the covariant derivative of the gravitational field eI, similarly to Lagrangian of scalar field in curved spacetime. Then, we discuss the case of free gravitational field. We find that this case takes place only in background spacetime approximation of low matter density; weak gravity. Similarly, we study the Plebanski two form complex field Σi and derive its Lagrangian with dependence only on the covariant derivative of Σi, which is represented in selfdual representation |Σi. Then, we try to combine the gravitational and Plebanski fields into one field: Kµi. Finally, we derive the static potential of exchanging gravitons between particles of scalar and spinor fields; the Newtonian gravitational potential. [ABSTRACT FROM AUTHOR]

A second-quantization treatment of the solution of the equation of classical mechanics is carried out. It is shown that all of the information about the multiparticle process of creation of a pair of scalar particles by a nonstationary potential barrier is contained in the solutions of Newton’s one-particle equation. The corresponding solution does not depend on Planck’s constant. It is shown that for any spatial quantum problem there exists a temporal classical analog. The obtained results can be used in quantum geometrodynamics. [ABSTRACT FROM AUTHOR]

A way to encode acceleration directly into fields has recently being proposed, thus establishing a new kind of fields, the accelerated fields. The definition of accelerated fields points to the quantization of space and time, analogously to the way quantities like energy and momentum are quantized in usual quantum field theories. Unruh effect has been studied in connection with quantum field theory in curved spacetime and it is described by recruiting a uniformly accelerated observer. In this work, as a first attempt to demonstrate the utility of accelerated fields, we present an alternative way to derive Unruh effect. We show, by studying quantum field theory on quantum spacetime, that Unruh effect can be obtained without changing the reference frame. Thus, in the framework of accelerated fields, the observational confirmation of Unruh effect could be assigned to the existence of quantum properties of spacetime. [ABSTRACT FROM AUTHOR]

In this series of papers, we investigate the projective framework initiated by Kijowski (1977) and Okołów (2009, 2014, 2013) [1,2] , which describes the states of a quantum theory as projective families of density matrices. A short reading guide to the series can be found in Lanéry (2016). A strategy to implement the dynamics in this formalism was presented in our first paper Lanéry and Thiemann (2017) (see also Lanéry, 2016, section 4), which we now test in two simple toy-models. The first one is a very basic linear model, meant as an illustration of the general procedure, and we will only discuss it at the classical level. In the second one, we reformulate the Schrödinger equation, treated as a classical field theory, within this projective framework, and proceed to its (non-relativistic) second quantization. We are then able to reproduce the physical content of the usual Fock quantization. [ABSTRACT FROM AUTHOR]

We investigate the perturbative aspects of Rozansky-Witten's 3d $${\sigma}$$ -model (Rozansky and Witten in Sel Math 3(3):401-458, 1997) using Costello's approach to the Batalin-Vilkovisky (BV) formalism (Costello in Renormalization and effective field theory, American Mathematical Society, Providence, 2011). We show that the BV quantization (in Costello's sense) of the model, which produces a perturbative quantum field theory, can be obtained via the configuration space method of regularization due to Kontsevich (First European congress of mathematics, Paris, 1992) and Axelrod-Singer (J Differ Geom 39(1):173-213, 1994). We also study the factorization algebra structure of quantum observables following Costello-Gwilliam (Factorization algebras in quantum field theory, Cambridge University Press, Cambridge 2017). In particular, we show that the cohomology of local quantum observables on a genus g handle body is given by $${H^*(X, (\wedge^*T_X)^{\otimes g})}$$ (where X is the target manifold), and we prove that the partition function reproduces the Rozansky-Witten invariants. [ABSTRACT FROM AUTHOR]

Into a geometric setting, we import the physical interpretation of index theorems via semi-classical analysis in topological quantum field theory. We develop a direct relationship between Fedosov's deformation quantization of a symplectic manifold X and the Batalin–Vilkovisky (BV) quantization of a one-dimensional sigma model with target X . This model is a quantum field theory of AKSZ type and is quantized rigorously using Costello's homotopic theory of effective renormalization. We show that Fedosov's Abelian connections on the Weyl bundle produce solutions to the effective quantum master equation. Moreover, BV integration produces a natural trace map on the deformation quantized algebra. This formulation allows us to exploit a (rigorous) localization argument in quantum field theory to deduce the algebraic index theorem via semi-classical analysis, i.e., one-loop Feynman diagram computations. [ABSTRACT FROM AUTHOR]

Exact solutions of relativistic quasipotential equations in the configuration representation were found for a system of two spin-1/2 quarks interacting via a Coulomb-like chromodynamical potential. Quantization conditions were found for the pseudoscalar, pseudovector, and vector cases. The present analysis was performed within the Hamiltonian formulation of quantum field theory via a transition to the relativistic configuration representation for the case of two relativistic spin-1/2 quarks of equal mass. [ABSTRACT FROM AUTHOR]

In this paper we study the stochastic quantization problem on the two dimensional torus and establish ergodicity for the solutions. Furthermore, we prove a characterization of the $${\Phi^4_2}$$ quantum field on the torus in terms of its density under translation. We also deduce that the $${\Phi^4_2}$$ quantum field on the torus is an extreme point in the set of all L-symmetrizing measures, where L is the corresponding generator. [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]

The quantization of proper (inherent) mass in microphysics is an essential quantization, which can be derived directly from Einstein field equation as well as from the ϕ4 theory in quantum field theory. This paper is written using only three parameters ħ, c, and G (gravitation constant). [ABSTRACT FROM AUTHOR]

In the current work, an analytical model for the design of vertically aligned silicon (Si) nanowire metal-oxide-semiconductor (MOS) capacitor based multi-color photodetectors has been developed for the detection of entire visible spectrum with high spectral resolution. The photogeneration phenomena within the nanostructures are analyzed in detail by developing a quantum field model associated with second quantization electron-photon field operators. The non-equilibrium Green's function (NEGF) formalism is employed to solve the relevant equations. The study shows that the proposed device with specified design of diameter-voltage combinations is capable of detecting 64 spectral bands of the entire visible spectrum (380 nm to700 nm) directly with a very high resolution of 5 nm wavelength. Such direct sensing of each wavelength is observed to be independent of the fluctuations of illumination intensity. The device is designed to obtain a full-width-at-half-maximum (FWHM) smaller than the spectral resolution (5 nm) for each wavelength of the visible range, which indicates a very high quality digital imaging/sensing method. Such devices may be a potential alternative for the future nanoelectronics based photodevices for superior sensing/imaging applications. [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]

Let G be a connected real semisimple Lie group having a finite center and a compact Cartan subgroup T with Lie algebra t0. Let ω be a G × T-invariant symplectic form on X = G × t0. We incorporate Dirac cohomology into the geometric quantization of (X , ω) and study the resulting multiplicity-free unitary G × T-representation on a Hilbert space H (X , ω). We also perform symplectic reduction of (X , ω) and show that our quantization method satisfies the principle “quantization commutes with reduction”. As an application we construct various models of discrete series. [ABSTRACT FROM AUTHOR]

The so-called Jackiw-Pi (JP) model for massive vector fields is a three-dimensional, gauge-invariant and parity-preserving model that was discussed in several contexts. In this paper we have discussed its quantum aspects through the introduction of Planck-scale objects, i.e., via noncommutativity and the well-known BV quantization. Namely, we have constructed the JP noncommutative space-time version, we have provided the BV quantization of the commutative JP model and we have discussed its features. The noncommutativity has introduced interesting new objects in JP's Planck-scale framework. [ABSTRACT FROM AUTHOR]

We study solutions of certain nonlinear Dirac-type equations on Riemann spin surfaces. We first improve an energy identity theorem for a sequence of such solutions with uniformly bounded energy in the case of a fixed domain. Then, we prove the corresponding energy identity in the case that the equations have constant coefficients and the domains possibly degenerate to a spin surface with only Neveu-Schwarz type nodes. [ABSTRACT FROM AUTHOR]

It is shown that the Dirac-Nambu-Goto brane can be described as a point particle in an infinite-dimensional brane space with a particular metric. This suggests a generalization to brane spaces with arbitrary metric, including the 'flat' metric. Then quantization of such a system is straightforward: it is just like quantization of a bunch of noninteracting particles. This leads us to a system of a continuous set of scalar fields. For a particular choice of the metric in the space of fields we find that the classical Dirac-Nambu-Goto brane theory arises as an effective theory of such an underlying quantum field theory. Quantization of branes is important for the brane world scenarios, and thus for 'quantum gravity.' [ABSTRACT FROM AUTHOR]

In the framework of Loop Quantum Cosmology (LQC), inhomogeneous models are usually quantized by means of a hybrid approach that combines loop quantization techniques with standard quantum field theory methods. This approach is based on a splitting of the phase space in a homogeneous sector, formed by global, zero-modes and an inhomogeneous sector, formed by the remaining, infinite number of modes, that describe the local degrees of freedom. Then, the hybrid quantization is attained by adopting a loop representation for the homogeneous gravitational sector, while a Fock representation is used for the inhomogeneities. The zero-mode of the Hamiltonian constraint operator couples the homogeneous and inhomogeneous sectors. The hybrid approach, therefore, is expected to provide a suitable quantum theory in regimes where the main quantum effects of the geometry are those affecting the zero-modes, while the inhomogeneities, still being quantum, can be treated in a more conventional way. This hybrid strategy was first proposed for the simplest cosmological midisuperspaces: the Gowdy models, and it has been later applied to the case of cosmological perturbations. This paper reviews the construction and main applications of hybrid LQC. [ABSTRACT FROM AUTHOR]

Polarization properties of Gaussian-Schell model quantization field propagating through the Kolmogorov turbulence of a marine-atmosphere channel are studied based on the degree of quantum polarization. The effective photon annihilation and creation operators of Gaussian-Schell model quantization field propagation in a marine-atmosphere are developed by making use of the extended Huygens-Fresnel integral of quantum field. The effects of the outer scale on the degree of polarization can be neglected. As the source transverse coherent width, the number of received photons, the inner scale of turbulent eddies, and the source transverse radius decrease or the refractive index structure parameter increases, the degree of polarization decreases. In theory, we find that the polarization fade of marine-atmosphere turbulence channels is larger than that of terrene -atmosphere turbulence channels under same transport parameters and the channel with a stronger turbulence strength will possess a larger detection area of a polarization signal, which have potentially important implications for free-space quantum key distribution. [ABSTRACT FROM AUTHOR]

The possibility that fundamental discreteness implicit in a quantum gravity theory may act as a natural regulator for ultraviolet singularities arising in quantum field theory has been intensively studied. Here, along the same expectations, we investigate whether a nonstandard representation called polymer representation can smooth away the large amount of negative energy that afflicts the Hamiltonians of higher-order time derivative theories, rendering the theory unstable when interactions come into play. We focus on the fourth-order Pais-Uhlenbeck model which can be reexpressed as the sum of two decoupled harmonic oscillators one producing positive energy and the other negative energy. As expected, the Schrödinger quantization of such model leads to the stability problem or to negative norm states called ghosts. Within the framework of polymer quantization we show the existence of new regions where the Hamiltonian can be defined well bounded from below. [ABSTRACT FROM AUTHOR]

I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de Broglie–Bohm and GRW interpretations. I further show that this interpretation-neutral, decoherence-based account conforms to a general view of inter-theoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified picture that treats reduction as a matter of simply taking limits. This interpretation-neutral account rests on a general three-pronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest׳s Theorem, and a decoherence-compatible mechanism for collapse. It also incorporates a novel argument as to why branch-relative trajectories should be approximately Newtonian, which is based on a little-discussed extension of Ehrenfest׳s Theorem to open systems, rather than on the more commonly cited but less germane closed-systems version. In the Conclusion, I briefly suggest how the strategy for quantum-classical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity. [ABSTRACT FROM AUTHOR]

In this work, we derive the asymptotic quasi-normal modes of a Banados-Teitelboim-Zanelli (BTZ) black hole using a quantum field theoretic Lagrangian. The BTZ black hole is a very popular system in the context of 2 + 1-dimensional quantum gravity. However, to our knowledge the quasi-normal modes of the BTZ black hole have been studied only in the classical domain. Here we show a way to quantize the quasi-normal modes of the BTZ black hole by mapping it to the Bateman-Feschbach-Tikochinsky oscillator and the Caldirola-Kanai oscillator. We have also discussed a couple of other black hole potentials to which this method can be applied. [ABSTRACT FROM AUTHOR]

We investigate stochastic quantization as a mathematical tool for quantum field theory. We test the method for the free scalar field. We find that the usual method of stochastic quantization is incompatible with establishing a Hilbert-space interpretation for transition probabilities in quantum theory. In particular, we prove that for any finite stochastic time, the standard probability measure violates reflection positivity. As a consequence, if one desires to use stochastic quantization in constructive quantum field theory, one needs to find a more robust procedure than the standard one. [ABSTRACT FROM AUTHOR]

We consider field quantization on an arbitrary null hypersurface in curved spacetime. We discuss the de Sitter horizon as the simplest example, relating the horizon quantization to the standard Fock space in the cosmological patch. We stress the universality of null-hypersurface kinematics, using it to generalize the Unruh effect to vacuum or thermal states with respect to null “time translations” on arbitrary (e.g. non-stationary) horizons. Finally, we consider a general pure state on a null hypersurface, which is divided into past and future halves, as when a bifurcation surface divides an event horizon. We present a closed-form recipe for reducing such a pure state into a mixed state on each half-hypersurface. This provides a framework for describing entanglement between spacetime regions directly in terms of their causal horizons. To illustrate our state-reduction recipe, we use it to derive the Unruh effect. [ABSTRACT FROM AUTHOR]

We use the framework of quantum field theory to obtain by deformation the Moyal-Weyl spacetime. This idea is extracted from recent progress in deformation theory concerning the emergence of the quantum plane of the Landau-quantization. The quantum field theoretical emerging spacetime is not equal to the standard Moyal-Weyl plane, but terms resembling relativistic corrections occur. [ABSTRACT FROM AUTHOR]

We investigate various aspects of invariance under local symmetries in the framework of perturbative algebraic quantum field theory (pAQFT). Our main result is the proof that the quantum Batalin-Vilkovisky operator, on-shell, can be written as the commutator with the interacting BRST charge. Up to now, this was proven only for a certain class of fields in quantum electrodynamics and in Yang-Mills theory. Our result is more general and it holds in a wide class of theories with local symmetries, including general relativity and the bosonic string. We also comment on other issues related to local gauge invariance and, using the language of homological algebra, we compare different approaches to quantization of gauge theories in the pAQFT framework. [ABSTRACT FROM AUTHOR]

Basis Light-front Quantization has been proposed as a nonperturbative framework for solving quantum field theory. We apply this approach to Quantum Electrodynamics and explicitly solve for the light-front wave function of a physical electron. Based on the resulting light-front wave function, we evaluate the electron anomalous magnetic moment. Nonperturbative mass renormalization is performed. Upon extrapolation to the infinite basis limit our numerical results agree with the Schwinger result obtained in perturbation theory to an accuracy of 0.06%. [ABSTRACT FROM AUTHOR]

In quantum field theory, elemental particles are assumed to be point particles. As a result, the loop integrals are divergent in many cases. Regularization and renormalization are necessary to get the physical finite results from the infinite, divergent loop integrations. We propose new quantization conditions for nonpoint particles. With this solid quantization, divergence could be treated systematically. This method is useful for effective field theory, which is on hadron degrees of freedom. The elemental particles could also be nonpoint ones. They can be studied in this approach as well. [ABSTRACT FROM AUTHOR]

We address some problem related to teaching quantum field theory at the university level. After a discussion of the pros and cons of the canonical quantization approach, we present an alternative teaching proposal. The novelty of this approach rests on the idea of using a multilevel structure, where the levels of phenomenology, formalism and interpretation are related but distinguishable. In this context, the quantization of the electromagnetic field, which is taken as a paradigmatic case in the standard approach, is addressed as a special case and studied only in the last step. [ABSTRACT FROM AUTHOR]

A physical interpretation of translation-invariant polarons and bipolarons is presented, some results of their existence are discussed. Consideration is given to the problem of quantization in the vicinity of the classical solution in the quantum field theory. The lowest variational estimate is obtained for the bipolaron energy E(η) with E(0) = -0.440636α, where α is a constant of electron-phonon coupling, η is a parameter of ion binding. [ABSTRACT FROM AUTHOR]

We study the 3-form gauge theory in the context of generalized BRST formulation. We construct the finite field-dependent BRST symmetry for such a theory. The generating functional for 3-form gauge theory in noncovariant gauge is obtained from that of covariant gauge. We further extend the results by considering 3-form gauge theory in the context of Batalin-Vilkovisky formulation. [ABSTRACT FROM AUTHOR]

We first review the spontaneous Lorentz symmetry breaking in the presence of mass-less gauge fields and infraparticles. This result was obtained long time ago in the context of rigorous quantum field theory (QFT) by Frohlich, Morchio and Strocchi [Ann. Phys. 119, 241 (1979); Phys. Lett. B 89, 61 (1979)] and reformulated by Balachandran and Vaidya (arXiv:1302.3406) using the notion of superselection sectors and direction-dependent test functions at spatial infinity for gauge transformations. Inspired by these developments and under the assumption that the spectrum of the electric charge is quantized (in units of a fundamental charge e). we construct a family of vertex operators which create winding number A;, electrically charged Abelian vortices from the vacuum (zero winding number sector) and/or shift the winding number by k units. Vortices created by this vertex operator may be viewed both as a source and as a probe for inducing and detecting the breaking of spontaneous Lorentz symmetry. We find that for rotating vortices, the vertex operator at level k shifts the angular momentum of the vortex by kq/q, where q is the electric charge of the quantum state of the vortex and q is the charge of the vortex scalar field under the U(l) gauge field. We also show that, for charged-particle-vortex composites, angular momentum eigenvalues shift by kq/q being the electric charge of the charged-particle-vortex composite. This leads to the result that for q/q half-odd integral and for odd k, our vertex operators flip the statistics of charged-particle-vortex composites from bosons to ferrnions and vice versa. For fractional values of q/q, application of vertex operator on charged-particle-vortex composite leads in general to composites with anyonic statistics. [ABSTRACT FROM AUTHOR]

We develop a quantization scheme for the vector potential on globally hyperbolic spacetimes which realizes it as a locally covariant conformal quantum field theory. This result allows us to employ on a large class of backgrounds, which are asymptotically flat at null infinity, a bulk-to-boundary correspondence procedure in order to identify for the underlying field algebra a distinguished ground state which is of Hadamard form. [ABSTRACT FROM AUTHOR]

Abstract: We revisit the coordinate coherent states approach through two different quantization procedures in the quantum field theory on the noncommutative Minkowski plane. The first procedure, which is based on the normal commutation relation between an annihilation and creation operators, deduces that a point mass can be described by a Gaussian function instead of the usual Dirac delta function. However, we argue this specific quantization by adopting the canonical one (based on the canonical commutation relation between a field and its conjugate momentum) and show that a point mass should still be described by the Dirac delta function, which implies that the concept of point particles is still valid when we deal with the noncommutativity by following the coordinate coherent states approach. In order to investigate the dependence on quantization procedures, we apply the two quantization procedures to the Unruh effect and Hawking radiation and find that they give rise to significantly different results. Under the first quantization procedure, the Unruh temperature and Unruh spectrum are not deformed by noncommutativity, but the Hawking temperature is deformed by noncommutativity while the radiation specturm is untack. However, under the second quantization procedure, the Unruh temperature and Hawking temperature are untack but the both spectra are modified by an effective greybody (deformed) factor. [Copyright &y& Elsevier]

Abstract: Time operator is studied on the basis of field quantization, where the difficulty stemming from Pauliʼs theorem is circumvented by borrowing ideas from the covariant quantization of the bosonic string, i.e., one can remove the negative energy states by imposing Virasoro constraints. Applying the index theorem, one can show that in a different subspace of a Fock space, there is a different self-adjoint time operator. However, the self-adjoint time operator in the maximal subspace of the Fock space can also represent the self-adjoint time operator in the other subspaces, such that it can be taken as the single, universal time operator. Furthermore, a new insight on Pauliʼs theorem is presented. [Copyright &y& Elsevier]

This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space). To start with, we discuss the Quantum Action Principle and provide evidence for its validity for non-commutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Z[ j] of connected Green functions makes sense (at least at one-loop level). Second, we consider the generalization of the BPHZ renormalization scheme to non-commutative field theories and apply it to the case of a self-interacting real scalar field: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization. [ABSTRACT FROM AUTHOR]

A general method to construct free quantum fields for massive particles of arbitrary definite spin in a canonical Hamiltonian framework is presented. The main idea of the method is as follows: a multicomponent Klein-Gordon field that satisfies canonical (anti)commutation relations and serves as an auxiliary higher spin field is introduced, and the physical higher spin field is obtained by acting on the auxiliary field by a suitable differential operator. This allows the calculation of the (anti)commutation relations, the Green functions and the Feynman propagators of the higher spin fields. In addition, canonical equations of motions, which are expressed in terms of the auxiliary variables, can be obtained also in the presence of interactions, if the interaction Hamiltonian operator is known. The fields considered transform according to the ( n/2, m/2)⊕( m/2, n/2) and ( n/2, m/2) representations of the Lorentz group. [ABSTRACT FROM AUTHOR]

A new concept of bootstrap in particle physics is proposed, which is fully compatible with the formalism of quantum field theory (QFT). The emergence of spacetime and the spectrum of elementary particles is discussed in this context. [ABSTRACT FROM AUTHOR]

We construct a consistent theory of a quantum massive Weyl field. We start with the formulation of the classical field theory approach for the description of massive Weyl fields. It is demonstrated that the standard Lagrange formalism cannot be applied for the studies of massive first-quantized Weyl spinors. Nevertheless we show that the classical field theory description of massive Weyl fields can be implemented in frames of the Hamilton formalism or using the extended Lagrange formalism. Then we carry out a canonical quantization of the system. The independent ways for the quantization of a massive Weyl field are discussed. We also compare our results with the previous approaches for the treatment of massive Weyl spinors. Finally the new interpretation of the Majorana condition is proposed. [ABSTRACT FROM AUTHOR]

The Faddeev-Jackiw canonical quantization formalism for constrained systems with Grassmann dynamical variables within the framework of the field theory is reviewed. First, by means of a iterative process, the symplectic supermatrix is constructed and their associated constraints are found. Next, by taking into account the phase space of the system, the constraint structure is considered. It is found that, if there are no auxiliary dynamical field variables, the supermatrix whose elements are the Bose-Fermi brackets between the constraints associated with the independent dynamical field variables coincides with the symplectic supermatrix corresponding to these independent variables. An alternative procedure to obtain the first-class constraints is given. It is shown that for systems with gauge symmetries, by means of suitable gauge-fixing conditions, a nonsingular final symplectic supermatrix can be found. Then, two possible ways of calculating the Faddeev-Jackiw brackets are pointed out. The relation between the Faddeev-Jackiw and Dirac brackets is discussed. Throughout the previous developments, the Faddeev-Jackiw and Dirac algorithms are compared. Finally, the Faddeev-Jackiw canonical quantization method is applied to a simple model and the obtained results are compared with the ones corresponding to the use of the Dirac procedure on this model. [ABSTRACT FROM AUTHOR]

We develop a quantization scheme for Maxwell's equations without source on an arbitrary oriented four-dimensional globally hyperbolic spacetime. The field strength tensor is the key dynamical object and it is not assumed a priori that it descends from a vector potential. It is shown that, in general, the associated field algebra can contain a non-trivial centre and, on account of this, such a theory cannot be described within the framework of general local covariance unless further restrictive assumptions on the topology of the spacetime are taken. [ABSTRACT FROM AUTHOR]

In this paper is considered relativistic quantum field theory expressed by elementary units of quantum information as they are considered as fundamental entity of nature by Carl Friedrich von Weizsaecker. Through quantization of a Weyl spinor describing an elementary unit of quantum information and consisting of four real components one obtains four pairs of creation and annihilation operators acting in a tensor space of states containing many units of quantum information. There can be constructed position and momentum operators from the creation and annihilation operators and based on these operators the Poincare group can be represented in this abstract tensor space of quantum information. A general state in the tensor space can be mapped to a state in Minkowski space-time by using the position representation of the eigenstates of the occupation number operators which correspond to the eigenstates of the harmonic oscillator. This yields a description of relativistic quantum mechanics. Quantization of the coefficients of a general state in the tensor space leads to many particle theory and thus to quantum field theory. [ABSTRACT FROM AUTHOR]

Abstract: We propose a new method for the nonperturbative solution of quantum field theories and illustrate its use in the context of a light-front analog to the Greenberg–Schweber model. The method is based on light-front quantization and uses the exponential-operator technique of the many-body coupled-cluster method. The formulation produces an effective Hamiltonian eigenvalue problem in the valence Fock sector of the system of interest, combined with nonlinear integral equations to be solved for the functions that define the effective Hamiltonian. The method avoids the Fock-space truncations usually used in nonperturbative light-front Hamiltonian methods and, therefore, does not suffer from the spectator dependence, Fock-sector dependence, and uncanceled divergences caused by such truncations. [Copyright &y& Elsevier]

U(1) Chern-Simons theory is quantized canonically on manifolds of the form $M = {\mathbb R}\times\Sigma$, where Σ is a closed orientable surface. In particular, we investigate the role of mapping class group of Σ in the process of quantization. We show that, by requiring the quantum states to form representation of the holonomy group and the large gauge transformation group, both of which are deformed by quantum effect, the mapping class group can be consistently represented, provided the Chern-Simons parameter k satisfies an interesting quantization condition. The representations of all the discrete groups are unique, up to an arbitrary sub-representation of the mapping class group. Also, we find a k↔1/k duality of the representations. [ABSTRACT FROM AUTHOR]

Rarita-Schwinger (RS) quantum free field is reexamined in the context of deformation quantization (DQ). It is interesting to consider this alternative for the specific case of the spin 3/2 field because DQ avoids the problem of dealing from the beginning with the extra degrees of freedom which appears in the conventional canonical quantization. It is found out that the subsidiary condition does not introduce any change either in the Wigner function or in other aspects of the Weyl-Wigner-Groenewold-Moyal formalism, such as: the Stratonovich-Weyl quantizer and normal ordering, in relation to de Dirac field case. The RS propagator is also calculated within this framework. [ABSTRACT FROM AUTHOR]

We study nonperturbative quantization of the first order formulation of three-dimensional gravity with positive cosmological constant (de Sitter space being the prototype vacuum solution, whose Euclideanization gives the three sphere) on the background topology of lens space, which is a three sphere modulo a discrete group. Instead of the strategy followed by a recent work [A. Castro. N. Lashkari, and A. Maloney, Phys. Rev. D 83, 124027 (2011); A. Castro, N. Lashkari, and A. Maloney Phys. Rev. D 84, 089904(E) (2011)], which compares results in the second and first order formulations of gravity, we concentrate solely on the latter. We note, as a striking feature, that the quantization which relies heavily on the axiomatic of topological quantum field theory, can only be consistently carried by augmenting the conventional theory by an additional topological term coupled through a dimensionless parameter. More importantly the introduction of this additional parameter renders the theory finite. [ABSTRACT FROM AUTHOR]

In this talk we discuss implications of the concept of the minimal length, the Planck length, for black hole physics, and argue, that it naturally leads to quantization of black hole area in Planck units. [ABSTRACT FROM AUTHOR]

Euclidean quantum gravity might be defined by stochastic quantisation that is governed by a higher order Langevin equation rather than a first order stochastic equation. In a transitory phase where the Lorentz time cannot be defined, the parameter that orders the evolution of quantum gravity phenomena is the stochastic time. This changes the definition of causality in the period of primordial cosmology. The prediction of stochastically quantised gravity is that there will a transition from an oscillating quantum phase to a semi-classical one, when the Lorentz time emerges. The end of the transition, as it can be observed from now and described by inflation models, is a diluted Universe, following the inflation phenomenological evolution. It is filled at the beginning with scattered classical primordial black holes. The smallest ones will quickly decay in matter, with a standard quantum field theory evolution till our period. The stable heavier black holes will remain, forming a good fraction of the dark matter and the large black holes observed in the galaxies. In a theoretically related way, this framework suggests the possibility of a gravitational parton content for "point-like" particles, in the same five dimensional quantum field theory context as in the primordial cosmology, with a (+ − − − −) signature for the 5d metrics. The very precise and explicit result expressed in this paper is actually far more modest than its motivation. We compute explicitly the meaning of a second order Langevin equation in zero dimensions and define precisely what is second order stochastic quantisation in a soluble case. [ABSTRACT FROM AUTHOR]

Recently, Bennett et al. (Eur. J. Phys. 37:014001, 2016) presented a physically-motivated and explicitly gauge-independent scheme for the quantisation of the electromagnetic field in flat Minkowski space. In this paper we generalise this field quantisation scheme to curved spacetimes. Working within the standard assumptions of quantum field theory and only postulating the physicality of the photon, we derive the Hamiltonian, H ^ , and the electric and magnetic field observables, E ^ and B ^ , respectively, without having to invoke a specific gauge. As an example, we quantise the electromagnetic field in the spacetime of an accelerated Minkowski observer, Rindler space, and demonstrate consistency with other field quantisation schemes by reproducing the Unruh effect. [ABSTRACT FROM AUTHOR]

The NHEG algebra is an extension of Virasoro introduced in [arXiv:1503.07861]; it describes the symplectic symmetries of (n + 4)-dimensional Near Horizon Extremal Geometries with SL(2, ℝ) × U(1)n+ 1 isometry. In this work we construct the NHEG group and classify the (coadjoint) orbits of its action on phase space. As we show, the group consists of maps from an n-torus to the Virasoro group, so its orbits are bundles of standard Virasoro coadjoint orbits over Tn. We also describe the unitary representations that are expected to follow from the quantization of these orbits, and display their characters. Along the way we show that the NHEG algebra can be built from u(1) currents using a twisted Sugawara construction. [ABSTRACT FROM AUTHOR]