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Gauge theories with general covariance are particularly reluctant to quantization. We discuss the example of the Hamiltonian formulation of the relativistic point particle that, despite its apparent simplicity, is of crucial importance since a number of point particle systems can be cast into this form on a higher dimensional Rindler background, as recently pointed out by Hojman. It is shown that this system can be equipped with a hidden local, symmetry generating, constraint which on the one hand does not bother the classical evolution and on the other hand simplifies the realization of the path integral quantization. Even though the positive impact of the hidden symmetry is more evident in the Lagrangian version of the theory, it is still present through the suggested Hamiltonian constraint.

We develop an approach to the study of Coulomb branch operators in 3D $\mathcal{N}=4$ gauge theories and the associated quantization structure of their Coulomb branches. This structure is encoded in a one-dimensional TQFT subsector of the full 3D theory, which we describe by combining several techniques and ideas. The answer takes the form of an associative and noncommutative star product algebra on the Coulomb branch. For `good' and `ugly' theories (according to the Gaiotto-Witten classification), we also exhibit a trace map on this algebra, which allows for the computation of correlation functions and, in particular, guarantees that the star product satisfies a truncation condition. This work extends previous work on abelian theories to the non-abelian case by quantifying the monopole bubbling that describes screening of GNO boundary conditions. In our approach, monopole bubbling is determined from the algebraic consistency of the OPE. This also yields a physical proof of the Bullimore-Dimofte-Gaiotto abelianization description of the Coulomb branch., Comment: 73 pages plus appendices; v2: improved presentation, updated references and acknowledgements, added comments and appendices; v3: fixed a reference, matches published version

We obtain the distribution amplitude (DA) of the pion from its light-front wave functions in the basis light-front quantization framework. This light-front wave function of the pion is given by the lowest eigenvector of a light-front effective Hamiltonian consisting a three-dimensional confinement potential and the color-singlet Nambu--Jona-Lasinion interaction both between the constituent quark and antiquark. The quantum chromodynamics (QCD) evolution of the DA is subsequently given by the perturbative Efremov-Radyushkin-Brodsky-Lepage evolution equation. Based on this DA, we then evaluate the singly and doubly virtual transition form factors in the space-like region for $\pi^0\rightarrow \gamma^*\gamma$ and $\pi^0\rightarrow \gamma^*\gamma^*$ processes using the hard-scattering formalism. Our prediction for the pion-photon transition form factor agrees well with data reported by the Belle Collaboration. However, in the large $Q^2$ region it deviates from the rapid growth reported by the BaBar Collaboration. Meanwhile, our result on the $\pi^0\rightarrow \gamma^*\gamma^*$ transition form factor is also consistent with other theoretical approaches and agrees with the scaling behavior predicted by perturbative QCD., Comment: 15 pages, 5 figures, 3 tables; figure 3 and corresponding discussions added; version accepted by PRD

International audience; In this paper, we propose a communication-efficiently decentralized machine learning framework that solves a consensus optimization problem defined over a network of inter-connected workers. The proposed algorithm, Censored and Quantized Generalized GADMM (CQ-GGADMM), leverages the worker grouping and decentralized learning ideas of Group Alternating Direction Method of Multipliers (GADMM), and pushes the frontier in communication efficiency by extending its applicability to generalized network topologies, while incorporating link censoring for negligible updates after quantization. We theoretically prove that CQ-GGADMM achieves the linear convergence rate when the local objective functions are strongly convex under some mild assumptions. Numerical simulations corroborate that CQ-GGADMM exhibits higher communication efficiency in terms of the number of communication rounds and transmit energy consumption without compromising the accuracy and convergence speed, compared to the censored decentralized ADMM, and the worker grouping method of GADMM.

Canonical quantization of gravitational systems is obstructed by the problem of time. Due to diffeomorphism symmetry the Hamiltonian vanishes: dynamics with respect to a background time parameter appears "frozen." Two strategies towards the quantization of such systems are the identification of a clock degree of freedom before quantization (deparametrization), and quantization on a kinematical Hilbert space which is subject to constraints (Dirac quantization). The usual canonical quantization in quantum field theory is analogous to deparametrization. Here we introduce a frozen formalism and Dirac quantization for a complex Klein-Gordon scalar field, and show that the resulting theory is equivalent to usual canonical quantization. We then apply the formalism to the group field theory formalism for quantum gravity, for which both deparametrization and a "timeless" quantization have been proposed in past work. We show how a frozen formalism for group field theory links between these two existing approaches, and illustrate in particular the construction of physical observables. We derive effective cosmological dynamics for group field theory in the new formalism and compare these to previous work. The frozen formalism could be extended to other approaches to quantum gravity that do not use a preferred time parameter., Comment: 17 pages, revtex two-column style; v2: extended discussion, minor typographical changes, updated references; version accepted in Physical Review D; v3: corrected a few typos, changed title to match journal publication title

Grant 62022031 Grant 61773135 Grant U20A20188 Backstepping method is a successful approach to deal with the systems in strict-feedback form. However, for networked control systems, the discontinuous virtual law caused by state quantization introduces huge challenges for its applicability. In this article, a quantized adaptive robust control approach in backsetpping framework is developed in this article for networked strict-feedback nonlinear systems with both state and input quantization. In order to prove the efficiency of the designed control scheme, a novel form of Lyapunov candidate function was constructed in the process of analyzing the stability, which is applicable for the systems with nondifferentiable virtual control law. In particular, the state and input quantizers can be in any form as long as they meet the sector-bound condition. The theoretic result shows that the tracking error is determined by the pregiven constants and quantization errors, which are also verified by the simulation results. publishersversion published

Formulations of magnetic monopoles in a Hilbert-space formulation of quantum mechanics require Dirac's quantization condition of magnetic charge, which implies a large value that can easily be ruled out for elementary particles by standard atomic spectroscopy. However, an algebraic formulation of non-associative quantum mechanics is mathematically consistent with fractional magnetic charges of small values. Here, spectral properties in non-associative quantum mechanics are derived, applied to the ground state of hydrogen with a magnetically charged nucleus. The resulting energy leads to new strong upper bounds for the magnetic charge of various elementary particles that can appear as the nucleus of hydrogen-like atoms, such as the muon or the antiproton., 25 pages

We carry out the Becchi-Rouet-Stora-Tyutin (BRST) quantization of the one (0 + 1)-dimensional (1D) model of a free massive spinning relativistic particle (i.e. a supersymmetric system) by exploiting its classical infinitesimal and continuous reparameterization symmetry transformations. We use the modified Bonora-Tonin (BT) supervariable approach (MBTSA) to BRST formalism to obtain the nilpotent (anti-)BRST symmetry transformations of the target space variables and the (anti-)BRST invariant Curci-Ferrari (CF)-type restriction for the 1D model of our supersymmetric (SUSY) system. The nilpotent (anti-)BRST symmetry transformations for other variables of our model are derived by using the (anti-)chiral supervariable approach (ACSA) to BRST formalism. Within the framework of the latter, we have shown the existence of the CF-type restriction by proving the (i) symmetry invariance of the coupled Lagrangians, and (ii) the absolute anticommutativity property of the conserved (anti-)BRST charges. The application of the MBTSA to a physical SUSY system (i.e. a 1D model of a massive spinning particle) is a novel result in our present endeavor. In the application of ACSA, we have considered only the (anti-)chiral super expansions of the supervariables. Hence, the observation of the absolute anticommutativity of the (anti-)BRST charges is a novel result. The CF-type restriction is universal in nature as it turns out to be the same for the SUSY and non-SUSY reparameterization (i.e. 1D diffeomorphism) invariant models of the (non-)relativistic particles., LaTeX file, 38 pages, version to appear in AHEP. arXiv admin note: text overlap with arXiv:2006.07874

The relationship between classical and quantum mechanics is usually understood via the limit ħ→0. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity with quantum mechanics and quantum field theory has challenged for many decades this basic idea. We recently showed (Bru and de Siqueira Pedra, 0000; Bru and de Siqueira Pedra, 2021 [46,47]) the emergence of classical dynamics for very general quantum lattice systems with mean-field interactions, without (complete) suppression of its quantum features, in the infinite volume limit. This leads to a theoretical framework in which the classical and quantum worlds are entangled. Such an entanglement is noteworthy and is a consequence of the highly non-local character of mean-field interactions. Therefore, this phenomenon should not be restricted to systems with mean-field interactions only, but should also appear in presence of interactions that are sufficiently long-range, yielding effective, classical background fields, in the spirit of the Higgs mechanism of quantum field theory. In order to present the result in a less abstract way than in its original version, here we apply it to a concrete, physically relevant, example and discuss, by this means, various important aspects of our general approach. The model we consider is not exactly solvable and the particular results obtained are new., CNPq (309723/2020-5), FAPESP (2017/22340- 9), as well as by the Basque Government through the grant IT641-13 and by the Spanish Ministry of Science, Innovation and Universities: MTM2017-82160-C2-2-P.

We explore the way different loop quantization prescriptions affect the formation of trapped surfaces in the gravitational collapse of a homogeneous dust cloud, with particular emphasis on the so-called μo scheme in which loop quantum cosmology was initially formulated. Its undesirable features in cosmological models led to the so-called improved dynamics or the μ¯ scheme. While the jury is still out on the right scheme for black hole spacetimes, we show that as far as black hole formation is concerned, the μo scheme has another, so far unknown, serious problem. We found that in the μo scheme, no trapped surfaces would form for a nonsingular collapse of a homogeneous dust cloud in the marginally bound case unless the minimum nonzero area of the loops over which holonomies are computed or the Barbero–Immirzi parameter decreases almost four times from its standard value. It turns out that the trapped surfaces in the μo scheme for the marginally bound case are also forbidden for an arbitrary matter content as long as the collapsing interior is isometric to a spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. We found that in contrast to the situation in the μo scheme, black holes can form in the μ¯ scheme, as well as other lattice refinements with a mass gap determined by quantum geometry.

International audience; The strange behavior of subatomic particles is described by quantum theory, whose standard interpretation rejected some fundamental principles of classical physics such as causality, objectivity, locality, realism and determinism. Recently, a granular relativistic electrodynamical model of the electron could capture the measured values of its observables and predict its mass from the stability of its substructure. The model involves numerous subparticles that constitute some tight nucleus and loosely bound envelope allegedly forming real waves. The present study examines whether such a substructure and associated dynamics allow fundamentally realist interpretations of emblematic quantum phenomena, properties and principles, such as wave-particle duality, loss of objectivity, quantization, simultaneous multipath exploration, collapse of wavepacket, measurement problem, and entanglement. Drawing inspiration from non-linear dynamical systems, subparticles would involve realist hidden variables while high-level observables would not generally be determined, as particles would generally be in unstable states before measurements. Quantum mechanics would constitute a high-level probabilistic description emerging from an underlying causal, objective, local, albeit contextual and unpredictable reality. Altogether, by conceiving particles as granular systems composed of numerous extremely sensitive fluctuating subcorpuscles, this study proposes the possible existence of a local fundamentally realist interpretation of quantum mechanics.

Primitive ontology is a recently much discussed approach to the ontology of quantum theory according to which the theory is ultimately about entities in 3-dimensional space and their temporal evolution. This paper critically discusses the primitive ontologies that have been suggested within the Bohmian approach to quantum field theory in the light of the existence of unitarily inequivalent representations. These primitive ontologies rely either on a Fock space representation or a wave functional representation, which are strictly speaking unambiguously available only for free systems in flat spacetime. As a consequence, it is argued that they do not constitute fundamental ontologies for quantum field theory, in contrast to the case of the Bohmian approach to quantum mechanics.

Polariton photoluminescence from cylindrical microcavities was studied under optical excitation below and above a nonlinear regime threshold. Lines of lateral excitonic polaritons quantization were observed in the spectra. In addition to quantization lines with a small orbital quantum number m, exciton-polariton whispering gallery modes with large m > 10 were observed in the cavities of relatively large diameter. In addition to the spectral distribution of the polariton size quantized modes, it was possible to observe their wavefunctions' spatial distribution.

Journal of high energy physics 09(9), 201 (1-80) (2021). doi:10.1007/JHEP09(2021)201, An integrable system is introduced, which is a generalization of the $ \mathfrak{sl} $(2) quantum affine Gaudin model. Among other things, the Hamiltonians are constructed and their spectrum is calculated using the ODE/IQFT approach. The model fits into the framework of Yang-Baxter integrability. This opens a way for the systematic quantization of a large class of integrable non-linear sigma models. There may also be some interest in terms of Condensed Matter applications, as the theory can be thought of as a multiparametric generalization of the Kondo model., Published by SISSA, [Trieste]

We analyzed recent experimental data on the disassembly of $^{28}$Si into 7$\alpha$ in terms of a hybrid $\alpha$-cluster model. We calculated the probability of breaking into several $\alpha$-like fragments for high $l$-spin values for identical and non-identical spin zero nuclei. Resonant energies were found for each $l$-value and compared to the data and other theoretical models. Toroidal-like structures were revealed in coordinate and momentum space when averaging over many events at high $l$. The transition from quantum to classical mechanics is highlighted., Comment: 16 pages, 15 figures

It is well-known that principal bundles and associated bundles underlie the geometric structure of classical gauge field theories. In this paper, we explore the reformulation of gauge theories in terms of Lie algebroids and their associated bundles. This turns out to be a simple but elegant change, mathematically involving a quotient that removes spurious structure. The payoff is that the entire geometric structure involves only vector bundles over space-time, and we emphasize that familiar concepts such as BRST are built into the geometry, rather than appearing as adjunct structure. Thus the formulation of gauge theories in terms of Lie algebroids provides a fully off-shell account of the BRST complex. We expect that this formulation will have appealing impacts on the geometric understanding of quantization and anomalies, as well as entanglement in gauge theories. The formalism covers all gauge theories, and we discuss Yang-Mills theories with matter as well as gravitational theories explicitly., SCOPUS: ar.j, info:eu-repo/semantics/published

In the presence of a periodic external drive, the mean value of the energy of a two-level quantum system (or qubit) displays the well-known Rabi oscillatory dynamics that is usually described within the rotating wave approximation. In order to calculate its standard deviation, we get rid of this latter and obtain a huge ratio (of order unity) of standard deviation over mean value. This is due to the large-amplitude high-frequency oscillations of the internal as well as of the overall phase of the two-level system. In presence of continuous measurement of, say, the ground state energy that yields the quantum Zeno effect, the system remains frozen in its ground state as long as the dynamics of the driven system allows its energy to stay within its Rabi standard deviation. When reaching the boundary, the energy suddenly flips over to the excited level in order to stay further within its standard deviation. We model this energy flip by use of parametrized quantum transitions and show that it can be defined as the result of action quantization. We check our theory by recovering the so-called “quantum jumps” published by Minev et al. (2019).

Deep learning has achieved outstanding results in various tasks in machine learning under the background of rapid increase in equipment’s computing capacity. However, while achieving higher performance and effects, model size is larger, training and inference time longer, the memory and storage occupancy increasing, the computing efficiency shrinking, and the energy consumption augmenting. Consequently, it’s difficult to let these models run on edge devices such as micro and mobile devices. Model compression technology is gradually emerging and researched, for instance, model quantization. Quantization aware training can take more accuracy loss resulting from data mapping in model training into account, which clamps and approximates the data when updating parameters, and introduces quantization errors into the model loss function. In quantization, we found that some stages of the two super-resolution model networks, SRGAN and ESRGAN, showed sensitivity to quantization, which greatly reduced the performance. Therefore, we use higher-bits integer quantization for the sensitive stage, and train the model together in quantization aware training. Although model size was sacrificed a little, the accuracy approaching the original model was achieved. The ESRGAN model was still reduced by nearly 67.14% and SRGAN model was reduced by nearly 68.48%, and the inference time was reduced by nearly 30.48% and 39.85% respectively. What’s more, the PI values of SRGAN and ESRGAN are 2.1049 and 2.2075 respectively.

20 pags., 12 figs., 2 tabs. -- This article belongs to the Special Issue Reactivity and Properties of Radicals and Radical Ions, We present path integral molecular dynamics (PIMD) calculations of an electron transfer from a heliophobic Cs dimer in its () state, located on the surface of a He droplet, to a heliophilic, fully immersed C molecule. Supported by electron ionization mass spectroscopy measurements (Renzler et al., J. Chem. Phys.2016, 145, 181101), this spatially quenched reaction was characterized as a harpoon-type or long-range electron transfer in a previous high-level ab initio study (de Lara-Castells et al., J. Phys. Chem. Lett.2017, 8, 4284). To go beyond the static approach, classical and quantum PIMD simulations are performed at 2 K, slightly below the critical temperature for helium superfluidity (2.172 K). Calculations are executed in the NVT ensemble as well as the NVE ensemble to provide insights into real-time dynamics. A droplet size of 2090 atoms is assumed to study the impact of spatial hindrance on reactivity. By changing the number of beads in the PIMD simulations, the impact of quantization can be studied in greater detail and without an implicit assumption of superfluidity. We find that the reaction probability increases with higher levels of quantization. Our findings confirm earlier, static predictions of a rotational motion of the Cs dimer upon reacting with the fullerene, involving a substantial displacement of helium. However, it also raises the new question of whether the interacting species are driven out-of-equilibrium after impurity uptake, since reactivity is strongly quenched if a full thermal equilibration is assumed. More generally, our work points towards a novel mechanism for long-range electron transfer through an interplay between nuclear quantum delocalization within the confining medium and delocalized electronic dispersion forces acting on the two reactants., This work has been partly supported by the Spanish Agencia Estatal de Investigación (AEI) and the Fondo Europeo de Desarrollo Regional (FEDER, UE) under Grant Nos. PID2020-114654GB I00, PID2020-117605GB-I00, FIS2017-83157-P, MAT2016-75354-P and by the Austrian Science Fund (FWF) under Grant P29893-N36

Theories with higher derivatives involve linear instabilities in the Hamiltonian commonly known as Ostrogradski ghosts and can be viewed as a very serious problem during quantization. To cure {this} , we have considered the properties of antilinearty that can be found inherently in the non-Hermitian Hamiltonians. Owing to the existence of antilinearity, we can construct an operator, called the $V$-operator, which acts as an intertwining operator between the Hamiltonian and its hermitian conjugate. We have used this $V$-operator to remove the linear momenta term from the higher derivative Hamiltonian by making it non-Hermitian in the first place via an isospectral similarity transformation. The final form of the Hamiltonian is free from the Ostrogradski ghosts under some restriction on the mass term., Comment: 12 pages, Latex, updated version

We consider an extension of the Standard Model that was proposed recently by one of the current authors (PQH), which admits magnetic monopoles with a mass of order of a few TeV. We impose, in addition to topological quantization in the SU(2) sector of the model, the Dirac Quantization Condition (DQC) required for consistency of the quantum theory of a charged electron in the presence of the monopole. This leads to the prediction ${\rm sin}^2\theta_W = 1/4$, where $\theta_W$ is the weak mixing angle at the energy scale set by the monopole mass. A leading-order renormalization-group analysis yields the value of ${\rm sin}^2 \theta_W \simeq 0.231$ at the $Z$-boson mass, as measured by experiment, under suitable conditions on the spectrum of the extra particles in the model., Comment: Amended version, to appear in Nucl. Phys. B, with several diverse arguments supporting the quantization of the weak mixing angle of the extended standard model in the presence of monopoles. References added. No effects on conclusions

We show how in the standard electroweak model three $SU(2)_L$ Nambu monopoles, each carrying electromagnetic (EM) and Z- magnetic fluxes, can merge (through Z-strings) with a single $U(1)_Y$ Dirac monopole to yield a composite monopole that only carries EM magnetic flux. Compatibility with the Dirac quantization condition requires this composite monopole to carry six quanta ($12 \pi /e$) of magnetic charge, independent of the electroweak mixing angle $\theta_w$. The Dirac monopole is not regular at the origin and the energy of the composite monopole is therefore divergent. We discuss how this problem is cured by embedding $U(1)_Y$ in a grand unified group such as $SU(5)$. A second composite configuration with only one Nambu monopole and a colored $U(1)_Y$ Dirac monopole that has minimal EM charge of $4\pi/e$ is also described. Finally, there exists a configuration with an EM charge of $8\pi/e$ as well as screened color magnetic charge., Comment: 4 pages, 2 figures; published (PRD) version

We develop a formalism to calculate the response of a model gravitational wave detector to a quantized gravitational field. Coupling a detector to a quantum field induces stochastic fluctuations ("noise") in the length of the detector arm. The statistical properties of this noise depend on the choice of quantum state of the gravitational field. We characterize the noise for vacuum, coherent, thermal, and squeezed states. For coherent states, corresponding to classical gravitational configurations, we find that the effect of gravitational field quantization is small. However, the standard deviation in the arm length can be enhanced -- possibly significantly -- when the gravitational field is in a non-coherent state. The detection of this fundamental noise could provide direct evidence for the quantization of gravity and for the existence of gravitons., Comment: 34 pages, 1 figure

Heat transport guided by the combined dynamics of surface phonon-polaritons (SPhPs) and phonons propagating in a polar nanowire is theoretically modeled and analyzed. This is achieved by solving numerically and analytically the Boltzmann transport equation for SPhPs and the Fourier’s heat diffusion equation for phonons. An explicit expression for the SPhP thermal conductance is derived and its predictions are found to be in excellent agreement with its numerical counterparts obtained for a SiN nanowire at different lengths and temperatures. It is shown that the SPhP heat transport is characterized by two fingerprints: (i) The characteristic quantum of SPhP thermal conductance independent of the material properties. This quantization appears in SiN nanowires shorter than 1 μm supporting the ballistic propagation of SPhPs. (ii) The deviation of the temperature profile from its typical linear behavior predicted by the Fourier’s law in absence of heat sources. For a 150 μm-long SiN nanowire maintaining a quasi-ballistic SPhP propagation, this deviation can be as large as 1 K, which is measurable by the current state-of-the-art infrared thermometers.

Both geometric and wave optical models, as well as classical and quantum mechanics, realize linear transformations with matrices, for plane optics, these are 2×2 and of unit determinant. Students and some researchers could assume that the structure of this matrix group is fairly evident and hardly interesting. However, the properties and applications even of this lowest 2×2 case are already unexpectedly rich. While in mechanics they cover classical angular momentum, quantum spin, and represent ‘2+1’ relativity, in optical models they lead from the geometrical description of light propagation in the paraxial regime to wave optics via linear canonical transforms requiring a more penetrating view of their manifold structure and multiple covers. The purpose of this review article is to highlight the topological space of 2×2 matrices as it applies to classical versus quantum and wave models, to underline how the latter requires the double cover of the former, thus using 2×2 matrices as an alternative viewpoint of the quantization process, beside the traditional characterization by commutation and non-commutations of position and momentum.

Many experiments and collected data support general relativity as it explains spacetime as a smooth Riemannian manifold. However, general relativity does not explain the chaotic nature of spacetime on the quantum level, where determinism is almost impossible. This is one of the major problems in physics yet it requires a deeper theory to solve this incompatibility. In this research, a derivation made from Newton’s law of gravitation to better explain the behavior of spacetime in the quantum world with the assumption that spacetime is quantized with energy wave-particles and these wave-particles accumulate to form massive wave like particles (hence the standard model of particle physics). In the end, the derivation and the assumption together clearly illustrate general relativity and quantum theory.

Canonical quantization (CQ) is built around $[Q,P]=i\hbar1\!\!1$, while affine quantization (AQ) is built around $[Q,D]=i\hbar\,Q$, where $D\equiv(PQ+QP)/2$. The basic CQ operators must fit $-\infty< P, Q, Comment: 6 pages; a simple introduction to affine quantization that even helps quantum gravity

Quantum aspects of black holes may have observational imprints on their absorption and emission spectrum. In this work, we consider the possibility of non-uniform area quantization and its effects on the phasing of gravitational waveform from coalescing black hole inspirals. These observations may provide detectable effects distinct from that of a uniform area quantization and allow us to put bounds on various parameters of the underlying model. Our work can also be regarded as a novel test for the area-entropy proportionality of black hole solutions in general relativity., 5 pages, 3 figures

We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed $D=4$ quantum inhomegeneous conformal Hopf algebras $\mathcal{U}_{\theta }(su(2,2)\ltimes T^{4}$) and $\mathcal{U}_{\bar{\theta}}(su(2,2)\ltimes\bar{T}^{4}$), where $T^{4}$ describe complex twistor coordinatesand $\bar{T}^{4}$ the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently we introduce the quantum deformations of $D=4$ Heisenberg-conformal algebra (HCA) $su(2,2)\ltimes H^{4,4}_\hslash$ ($H^{4,4}_\hslash=\bar{T}^4 \ltimes_\hslash T_4$ is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length $\lambda_p$ will be called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We shall describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and by the quantization map in $H_\hslash^{4,4}$. We introduce as well generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra $\mathcal{U}_\theta(su(2,2)\ltimes T^4).$, Comment: 23 pages; Dedicated on 90-th Birthday to Sir Roger Penrose as a tribute to his ideas and achievements,{Submitted to Special Issue of SYMMETRY "Quantum Group Symmetry and Quanatum Geometry", ed. A. Ballesteros, G. Gubitosi, F.J. Herranz (2021)}; v2-as published on 15.07.2021 in SYMMETRY

We describe a systematic method to construct models of Chern insulators whose Berry curvature and the quantum volume form coincide and are flat over the Brillouin zone; such models are known to be suitable for hosting fractional Chern insulators. The bands of Chern insulator models where the Berry curvature and the quantum volume form coincide, and are nowhere vanishing, are known to induce the structure of a K\"ahler manifold in momentum space, and thus we are naturally led to define K\"ahler bands to be Chern bands satisfying such properties. We show how to construct a geometrically flat K\"ahler band, with Chern number equal to minus the total number of bands in the system, using the idea of K\"ahler quantization and properties of Bergman kernel asymptotics. We show that, with our construction, the geometrical properties become flatter as the total number of bands in the system is increased; we also show the no-go theorem that it is not possible to construct geometrically perfectly flat K\"ahler bands with a finite number of bands. We give an explicit realization of this construction in terms of theta functions and numerically confirm how the constructed K\"ahler bands become geometrically flat as we increase the number of bands. We also show the effect of truncating hoppings at a finite length, which will generally result in deviation from a perfect K\"ahler band but does not seem to seriously affect the flatness of the geometrical properties., Comment: 17 pages, 3 figures; closer to published version

We study canonical and affine versions of the quantized covariant Euclidean Higgs scalar field-theory for two real fields on four dimensional lattices through the Monte Carlo method. We calculate the two-point function near the continuum limit at finite volume., 18 pages, 6 figures. arXiv admin note: text overlap with arXiv:2103.06746

Whether gravity is quantized remains an open question. To shed light on this problem, various Gedankenexperiments have been proposed. One popular example is an interference experiment with a massive system that interacts gravitationally with another distant system, where an apparent paradox arises: even for space-like separation the outcome of the interference experiment depends on actions on the distant system, leading to a violation of either complementarity or no-signalling. A recent resolution shows that the paradox is avoided when quantizing gravitational radiation and including quantum fluctuations of the gravitational field. Here we show that the paradox in question can also be resolved without considering gravitational radiation, relying only on the Planck length as a limit on spatial resolution. Therefore, in contrast to conclusions previously drawn, we find that the necessity for a quantum field theory of gravity does not follow from so far considered Gedankenexperiments of this type. In addition, we point out that in the common realization of the setup the effects are governed by the mass octopole rather than the quadrupole. Our results highlight that no Gedankenexperiment to date compels a quantum field theory of gravity, in contrast to the electromagnetic case., 5 pages, 1 figure

A conformally invariant model of two interacting massless particles in Minkowski space was proposed by Casalbuoni and Gomis [1]. We generalize this model to the case of de Sitter space from the perspective of geodesic distance, in such a way that the resulting, generalized action reduces to the original action in a limit that de Sitter radius goes to infinity. We analyze the Hamiltonian formulation in accordance with Dirac's prescription for constrained Hamiltonian systems and carry out its subsequent canonical quantization in coordinate representation following DeWitt. As the result, we derive a fourth-order differential wave equation for bilocal fields that, in the infinite radius limit, reproduces one obtained in the original model for Minkowski space case., 7pages, main result and overall exposition significantly improved, title changed, references added, version to be published in PLB

This paper gives both the solutions to the puzzles of quantum gravity and a general theory of quantum gravity, further shows quantum gravity of the Universe and general black hole, and discovers their relations reflecting symmetric propertis of the standard nonlinear gravitational Lagrangian, which are not relevant to any concrete metric models. This paper concretely shows the general commutation relations of the general gravitational field operators and their zeroth, first, second and third style, respectively, of high order canonical momentum operators for the general nonlinear system of the standard gravitational Lagrangian, and then has finished all the four styles of the quantization of the standard gravity. No needing, as usual, to solve the Euler-Lagrange equation to complete the whole process of the quantization of the standard gravitational fields, namely, this paper novelly simplifies all the current quantization theories of the standard gravitational fields. So lots of the complex calculations of quantum gravitational field theories up to now can be omitted to make the physical picture clearer, simpler and more easily understanding. Therefore, the solutions to puzzles of quantum gravity are given. Consequently, this paper opens a door to study and give a general theory of the quantum gravitational field don't depending on any concrete metric models.

Topological edge states exhibit dissipationless transport and electrically-driven topological phase transitions, making them ideal for next-generation transistors that are not constrained by Moore's law. Nevertheless, their dispersion has never been probed and is often assumed to be simply linear, without any rigorous justification. Here we determine the non-linear electrical response of topological edge states in the ballistic regime and demonstrate the way this response ascertains the presence of symmetry breaking terms in the edge dispersion, such as deviations from non-linearity and tilted spin quantization axes. The non-linear response stems from discontinuities in the band occupation on either side of a Zeeman gap, and its direction is set by the spin orientation with respect to the Zeeman field. We determine the edge dispersion for several classes of topological materials and discuss experimental measurement., 8 pages, 4 figures

We give an overview of the work done during the past ten years on the Casimir interaction in electronic topological materials, our focus being solids which possess surface or bulk electronic band structures with nontrivial topologies, which can be evinced through optical properties that are characterizable in terms of nonzero topological invariants. The examples we review are three-dimensional magnetic topological insulators, two-dimensional Chern insulators, graphene monolayers exhibiting the relativistic quantum Hall effect, and time reversal symmetry-broken Weyl semimetals, which are fascinating systems in the context of Casimir physics, firstly for the reason that they possess electromagnetic properties characterizable by axial vectors (because of time reversal symmetry breaking), and depending on the mutual orientation of a pair of such axial vectors, two systems can experience a repulsive Casimir-Lifshitz force even though they may be dielectrically identical. Secondly, the repulsion thus generated is potentially robust against weak disorder, as such repulsion is associated with a Hall conductivity which is topologically protected in the zero-frequency limit. Finally, the far-field low-temperature behavior of the Casimir force of such systems can provide signatures of topological quantization., Comment: 32 pages, 7 figures, and 2 tables

Susskind-Glogower coherent states, whose Fock expansion coefficients include Bessel functions, have recently attracted considerable attention for their optical properties. Nevertheless, identity resolution is still an open question, which is an essential mathematical property that defines an overcomplete basis in the Fock space and allows a coherent state quantization map. In this regard, the modified Susskind-Glogower coherent states have been introduced as an alternative family of states that resolve the identity resolution. In the present manuscript, the quantization map related to the modified Susskind-Glogower coherent states is exploited, which naturally leads to a particular representation of the $\mathfrak{su}(1,1)$ Lie algebra in its discrete series. The latter provides evidence about further generalizations of coherent states, built from the Susskind-Glogower ones by extending the indexes of the Bessel functions of the first kind and, alternatively, by employing the modified Bessel functions of the second kind. In this form, the new families of Susskind-Glogower-I and Susskind-Glogower-II coherent states are introduced. The corresponding quantization maps are constructed so that they lead to general representations of elements of the $\mathfrak{su}(1,1)$ and $\mathfrak{su}(2)$ Lie algebras as generators of the SU$(1,1)$ and SU$(2)$ unitary irreducible representations respectively. For completeness, the optical properties related to the new families of coherent states are explored and compared with respect to some well-known optical states.