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We give a brief overview how to couple general relativity to the Standard Model of elementary particles, within the higher gauge theory framework, suitable for the spinfoam quantization procedure. We begin by providing a short review of all relevant mathematical concepts, most notably the idea of a categorical ladder, 3-groups and generalized parallel transport. Then, we give an explicit construction of the algebraic structure which describes the full Standard Model coupled to Einstein-Cartan gravity, along with the classical action, written in the form suitable for the spinfoam quantization procedure. We emphasize the usefulness of the 3-group concept as a superior tool to describe gauge symmetry, compared to an ordinary Lie group, as well as the possibility to employ this new structure to classify matter fields and study their spectrum, including the origin of fermion families. [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]

A relation between the precanonical quantization of pure Yang–Mills fields and the standard functional Schrödinger representation in the temporal gauge is established. It is shown that the latter can be obtained from the former when the ultraviolet parameter ϰ introduced in precanonical quantization goes to infinity. In this limiting case, the Schrödinger wave functional can be expressed as the trace of the Volterra product integral of Clifford-algebra-valued precanonical wave functions restricted to a field configuration, and the canonical functional derivative Schrödinger equation together with the quantum Gauss constraint is derived from the Dirac-like precanonical Schrödinger equation. [ABSTRACT FROM AUTHOR]

We derive the formula of the entanglement entropy between the left and right oscillating modes of the σ -model with the de Sitter target space. To this end, we study the theory in the cosmological gauge in which the non-vanishing components of the metric on the two-dimensional base space are functions of the expansion parameter of the de Sitter space. The model is embedded in the causal north pole diamond of the Penrose diagram. We argue that the cosmological gauge is natural to the σ -model as it is compatible with the canonical quantization relations. In this gauge, we obtain a new general solution to the equations of motion in terms of time-independent oscillating modes. The constraint structure is adequate for quantization in the Gupta–Bleuler formalism. We construct the space of states as a one-parameter family of Hilbert spaces and give the Bargmann–Fock and Jordan–Schwinger representations of it. Also, we give a simple description of the physical subspace as an infinite product of D 1 2 + in the positive discreet series irreducible representations of the S U ( 1 , 1 ) group. We construct the map generated by the Hamiltonian between states at two different values of time and show how it produces the entanglement of left and right excitations. Next, we derive the formula of the entanglement entropy of the reduced density matrix for the ground state acted upon by the Hamiltonian map. Finally, we determine the asymptotic form of the entanglement entropy of a single mode bi-oscillator in the limit of large values of time. [ABSTRACT FROM AUTHOR]

Chamseddine and Mukhanov showed that gravity and gauge theories could be unified in one geometric construction provided that a metricity condition is imposed on the vielbein. In this paper we are going to show that by enlarging the gauge group we are able to unify Chern-Simons gauge theory and Chern-Simons gravity in 3-D space-time. Such a unification leads to the quantization of the coefficients for both Chern-Simons terms for compact groups but not for non-compact groups. Moreover, it leads to a topological invariant quantity of the 3-dimensional space-time manifold on which they are defined. [ABSTRACT FROM AUTHOR]

The gauged model of Siegel type chiral boson is considered. It has been shown that the action of gauged model of Floreanini–Jackiw (FJ) type chiral boson is contained in it in an interesting manner. A BRST invariant action corresponding to the action of gauged FJ type chiral boson has been formulated using Batalin, Fradkin and Vilkovisky based improved Fujiwara, Igarishi and Kubo (FIK) formalism. An alternative quantization of the gauge symmetric action has been made with a Lorentz gauge and an attempt has been made to establish the equivalence between the gauge symmetric version of the extended phase space and original gauge non-invariant version of the usual phase space. [ABSTRACT FROM AUTHOR]

In this paper we study the existence of vortex-type solutions for a system of self-dual equations deduced from the mass-deformed Aharony-Bergman-Jafferis-Maldacena (ABJM) model. The governing equations, derived by Mohammed, Murugan, and Nastse under suitable ansatz involving fuzzy sphere matrices, have the new feature that they can support only non-topological vortex solutions. After transforming the self-dual equations into a nonlinear elliptic $${2\times 2}$$ system we prove first an existence result by means of a perturbation argument based on a new and appropriate scaling for the solutions. Subsequently, we prove a more complete existence result by using a dynamical analysis together with a blow-up argument. In this way we establish that any positive energy level is attained by a 1-parameter family of vortex solutions, which also correspond to (constraint) energy minimizers. In other words, we register the exceptional fact in a BPS-setting that, neither a 'quantization' effect nor an energy gap is induced upon the system by the rigid 'critical' coupling of the self-dual regime. [ABSTRACT FROM AUTHOR]

We consider $$ \mathcal{N}=2 $$ SU(2) gauge theories in four dimensions (pure or mass deformed) and discuss the properties of the simplest chiral observables in the presence of a generic Ω-deformation. We compute them by equivariant localization and analyze the structure of the exact instanton corrections to the classical chiral ring relations. We predict exact relations valid at all instanton number among the traces 〈Tr φ 〉, where φ is the scalar field in the gauge multiplet. In the Nekrasov-Shatashvili limit, such relations may be explained in terms of the available quantized Seiberg-Witten curves. Instead, the full two-parameter deformation enjoys novel features and the ring relations require non trivial additional derivative terms with respect to the modular parameter. Higher rank groups are briefly discussed emphasizing non-factorization of correlators due to the Ω-deformation. Finally, the structure of the deformed ring relations in the $$ \mathcal{N} = {2}^{\star } $$ theory is analyzed from the point of view of the Alday-Gaiotto-Tachikawa correspondence proving consistency as well as some interesting universality properties. [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]

A gauge fixing condition is presented here for non-Abelian gauge theory on the manifold R ⊗ S 1 ⊗ S 1 ⊗ S 1 . It is proved that the new gauge fixing condition is continuous and free from the Gribov ambiguity. While perturbative calculations based on the new gauge condition behave like those based on the axial gauge in ultraviolet region, infrared behaviours of the perturbative series under the new gauge fixing condition are quite nontrivial. The new gauge condition, which reads n ⋅ ∂ n ⋅ A = 0 , may not satisfy the boundary condition A μ ( ∞ ) = 0 as required by conventional perturbative calculations for gauge theories on the manifold S 4 . However, such contradiction is not harmful for the theory considered here. [ABSTRACT FROM AUTHOR]

In this paper the subject of the BRST symmetry representation by means of superfields is resumed and extended to N = 1 supersymmetric gauge theories. Then a new extension to diffeomorphisms is presented. Finally some speculations of a possible global representation of BRST symmetric theories by means of non-trivial supermanifolds are outlined. [ABSTRACT FROM AUTHOR]

It is shown that, anti-BRST symmetry is the quantized counterpart of local axial symmetry in gauge theories. An extended form of descent equations is worked out, which yields a set of modified consistent anomalies. [ABSTRACT FROM AUTHOR]

In this talk we study the light-front quantization of the restricted gauge theory of QCD à la Cho et al. [ABSTRACT FROM AUTHOR]

Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism. [ABSTRACT FROM AUTHOR]

In this talk, we study the light-front quantization of the vector Schwinger model with photon mass term in Faddeevian Regularization, describing two-dimensional electrodynamics with mass-less fermions but with a mass term for the U(1) gauge field. This theory is gauge-non-invariant (GNI). We construct a gauge-invariant (GI) theory using Stueckelberg mechanism and then recover the physical content of the original GNI theory from the newly constructed GI theory under some special gauge-fixing conditions (GFC's). We then study LFQ of this new GI theory. [ABSTRACT FROM AUTHOR]

We make a gauge theory from the Open p-brane system and map it into the Open 2-Brane one. Due to the presence of second-class constraints in this model, we encounter some problems during the procedure of quantization. In this regard, considering boundary conditions as Dirac conditions, one can drive the constrained structure of the model at first. Then, with the help of BFT formalism of constraint systems, the Open 2-Brane model is embedded into an extended phase space. For this purpose, we introduce some tensor fields to convert ungauged theory into the gauged one. This is the novel part of our research, while mostly scalar and vector fields are used to convert second-class constraints into first ones. [ABSTRACT FROM AUTHOR]

The Dirac procedure for dealing with constraints is applied to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first-class constraints that arise and the resulting Dirac brackets are found. These gauge conditions are not used to eliminate degrees of freedom from the action prior to applying the Dirac constraint procedure. This approach is illustrated by considering Yang-Mills theory and the superparticle in a 2+1-dimensional target space. [ABSTRACT FROM AUTHOR]

We develop a new version of the superfield Hamiltonian quantization. The main new feature is that the BRST-BFV charge and the gauge fixing Fermion are introduced on equal footing within the sigma model approach, which provides for the actual use of the quantum/derived antibrackets. We study in detail the generating equations for the quantum antibrackets and their primed counterparts. We discuss the finite quantum anticanonical transformations generated by the quantum antibracket. [ABSTRACT FROM AUTHOR]

We investigate the non-Abelian Aharonov–Bohm (AB) effect for time-dependent gauge fields. We prove that the non-Abelian AB phase shift related to time-dependent gauge fields, in which the electric and magnetic fields are written in the adjoint representation of SU ( N ) generators, vanishes up to the first order expansion of the phase factor. Therefore, the flux quantization in a superconductor ring does not appear in the time-dependent Abelian or non-Abelian AB effect. [ABSTRACT FROM AUTHOR]

In the presence of electric and gauge fields, it is possible to have effective charges, where an electron attached to an electric field flux can be termed a composite charge. Using the similar configuration of hydrogen, we calculate quantized energy eigenvalues for lattice ions, where the effective charge of an electron can assume a value of 0e or −2e and may be regarded as a photon composite; furthermore, polaritons from these composites can be quantized. We also compare our energy levels with experimental data obtained from inelastic neutron scatterings, in which the data above ∼ 3 meV ( = 24.1966 cm−1) may be attributed to phonon modes in ferroelectric Rochelle salt. [ABSTRACT FROM AUTHOR]

We have embedded the nonlinear sigma model in a non-Abelian gauge theory. After that as a first class-system, it was quantized using two different approaches: the functional Schrödinger method and the nonlocal field-antifield procedure. First, the quantization was performed with the functional Schrödinger method, for , obtaining the wave functionals for the ground and excited states. Second, using the well-known BV formalism, we have computed the one-loop anomaly. This result shows that the classical gauge symmetries, which appear due to the conversion via BFFT method, are broken at the quantum level. [ABSTRACT FROM AUTHOR]

We show that the Hamiltonian HQ, introduced in the course of BRST analysis of a gauge theory, may in fact be associated with an action that itself is gauge invariant. This action can then be treated using the BRST formalism. We illustrate this by considering the spinning particle and the first-order Einstein-Hilbert action in 1 + 1 dimensions. [ABSTRACT FROM AUTHOR]

Let X be a smooth algebraic variety over a field K containing the real numbers. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf O X . These are stack-like versions of usual deformations. We prove that there is a twisted quantization operation from twisted Poisson deformations to twisted associative deformations, which is canonical and bijective on gauge equivalence classes. This result extends work of Kontsevich, and our own earlier work, on deformation quantization of algebraic varieties. [ABSTRACT FROM AUTHOR]

We propose a group-theoretical interpretation of the fact that the transition from classical to quantum mechanics entails a reduction in the number of observables needed to define a physical state (e.g. from $$q$$ and $$p$$ to $$q$$ or $$p$$ in the simplest case). We argue that, in analogy to gauge theories, such a reduction results from the action of a symmetry group. To do so, we propose a conceptual analysis of formal tools coming from symplectic geometry and group representation theory, notably Souriau's moment map, the Mardsen-Weinstein symplectic reduction, the symplectic 'category' introduced by Weinstein, and the conjecture (proposed by Guillemin and Sternberg) according to which 'quantization commutes with reduction'. By using the generalization of this conjecture to the non-zero coadjoint orbits of an abelian Hamiltonian action, we argue that phase invariance in quantum mechanics and gauge invariance have a common geometric underpinning, namely the symplectic reduction formalism. This stance points towards a gauge-theoretical interpretation of Heisenberg indeterminacy principle. We revisit (the extreme cases of) this principle in the light of the difference between the set-theoretic points of a phase space and its category-theoretic symplectic points. [ABSTRACT FROM AUTHOR]

We construct a gauge theory on a noncommutative homogeneous Kähler manifold, wherewe employ the deformation quantizationwith separation of variables for Kähler manifolds formulated by Karabegov. A key point in this construction is to obtaining vector fields which act as inner derivations for the deformation quantization. We give an explicit construction of this gauge theory on noncommutative CPN and noncommutative CHN. [ABSTRACT FROM AUTHOR]

Abstract: We suggest a minimal extension of the standard model, which can explain current experimental data of the dark matter, small neutrino masses and baryon asymmetry of the universe, inflation, and dark energy, and achieve gauge coupling unification. The gauge coupling unification can explain the charge quantization, and be realized by introducing six new fields. We investigate the vacuum stability, coupling perturbativity, and correct dark matter abundance in this model by use of current experimental data. [Copyright &y& Elsevier]

Abstract: Quantization theory gives rise to transverse phonons for the traditional Coulomb gauge condition and to scalar and longitudinal photons for the Lorentz gauge condition. We describe a new approach to quantize the general singular QED system by decomposing a general gauge potential into two orthogonal components in general field theory, which preserves scalar and longitudinal photons. Using these two orthogonal components, we obtain an expansion of the gauge-invariant Lagrangian density, from which we deduce the two orthogonal canonical momenta conjugate to the two components of the gauge potential. We then obtain the canonical Hamiltonian in the phase space and deduce the inherent constraints. In terms of the naturally deduced gauge condition, the quantization results are exactly consistent with those in the traditional Coulomb gauge condition and superior to those in the Lorentz gauge condition. Moreover, we find that all the nonvanishing quantum commutators are permanently gauge-invariant. A system can only be measured in physical experiments when it is gauge-invariant. The vanishing longitudinal vector potential means that the gauge invariance of the general QED system cannot be retained. This is similar to the nucleon spin crisis dilemma, which is an example of a physical quantity that cannot be exactly measured experimentally. However, the theory here solves this dilemma by keeping the gauge invariance of the general QED system. [Copyright &y& Elsevier]

The quantization of Yang-Mills theories relies on the gauge-fixing procedure. However, in the non-Abelian case this procedure leads to the well-known Gribov ambiguity. In order to solve the ambiguity a modification of the functional integral formula must be introduced. As a consequence of this, the Green functions get deep modifications in the infrared. We consider, in particular, the (N) case and show that in the pure gauge case the ghost propagator is enhanced, while the gluon propagator is suppressed in this limit, therefore the study of the Gribov ambiguity may shed some light on the mass gap problem and on color confinement. We discuss some recent developments on the subject in the case of a curved background. We argue that the concurrent presence of a spacetime curvature and the Gribov ambiguity may introduce further modifications to the Green functions in the infrared. [ABSTRACT FROM AUTHOR]

We propose a mechanism displaying confinement, as defined by the behavior of the propagators, for four-dimensional, N = 1 supersymmetric Yang–Mills theory in superfield formalism. In this work we intend to verify the possibility of extending the known Gribov problem of quantization of Yang–Mills theories and the implementation of a local action with auxiliary superfields, like the Gribov–Zwanziger approach, to this problem. [ABSTRACT FROM AUTHOR]

Abstract: We quantize the bosonic part of the string with closed boundary conditions on the light cone and we consider the worldsheet gauge field a dynamical variable. We compute also 3-Reggeon vertex by the overlapping technique. We find that the Fock space is the sum of sectors characterized by the momentum of the Wilson line and that these sectors do not interact among them. Each sector has exactly the same spectrum of the usual bosonic string when expressed in properly sector dependent rescaled variables. Rescaling is forced by factorization of the string amplitudes. We are also able to determine the relative string coupling constant of the different sectors. It follows a somewhat unexpected picture in which the effective action is always the same independently on the sector but string amplitudes are only the same when expressed in sector dependent rescaled variables. [Copyright &y& Elsevier]

The surface of a 3+1d-topological insulator hosts an odd number of gapless Dirac fermions when charge conjugation and time-reversal symmetries are preserved. Viewed as a purely 2+1d system, this surface theory would necessarily explicitly break parity and time-reversal when coupled to a fluctuating gauge field. Here, we explain why such a state can exist on the boundary of a 3+1d system without breaking these symmetries, even if the number of boundary components is odd. This is accomplished from two complementary perspectives: topological quantization conditions and regularization. We first discuss the conditions under which (continuous) large gauge transformations may exist when the theory lives on a boundary of a higher-dimensional space-time. Next, we show how the higher-dimensional bulk theory is essential in providing a parity-invariant regularization of the theory living on the lower-dimensional boundary or defect. [ABSTRACT FROM AUTHOR]

Shape dynamics is a gauge theory based on spatial diffeomorphism- and Weyl-invariance which is locally indistinguishable from classical general relativity. If taken seriously, it suggests that the space-time geometry picture that underlies general relativity can be replaced by a picture based on spatial conformal geometry. This classically well-understood trading of gauge symmetries opens new conceptual avenues in many approaches to quantum gravity. This paper focusses on the general implications for quantum gravity and effective field theory and considers the application of the shape dynamics picture in the exact renormalization group approaches to gravity, loop- and polymer-quantization approaches to gravity and low energy effective field theories. Also, the interpretation of known results is discussed through the shape dynamics picture, particularly holographic renormalization and the problem of time in canonical quantum gravity. [ABSTRACT FROM AUTHOR]