Gauge Field Theory Research Articles

An important class of conformally flat weak Einstein cubic (α,β)-metrics

The theory of cubic metrics plays an important role in the theory of space-time structure, gravitation and unified gauge field theories. In this paper, we study conformally flat weak Einstein cubic [Formula: see text]-metrics. We prove that such metrics must be either locally Minkowski metric or Riemannian metric.

Variational Discretizations of Gauge Field Theories Using Group-Equivariant Interpolation

We describe a systematic mathematical approach to the geometric discretization of gauge field theories that is based on Dirac and multi-Dirac mechanics and geometry, which provide a unified mathematical framework for describing Lagrangian and Hamiltonian mechanics and field theories, as well as degenerate, interconnected, and nonholonomic systems. Variational integrators yield geometric structure-preserving numerical methods that automatically preserve the symplectic form and momentum maps, and exhibit excellent long-time energy stability. The construction of momentum-preserving variational integrators relies on the use of group-equivariant function spaces, and we describe a general construction for functions taking values in symmetric spaces. This is motivated by the geometric discretization of general relativity, which is a second-order covariant gauge field theory on the symmetric space of Lorentzian metrics.

Modern Physics of the Condensed State: Strong Correlations and Quantum Topology

The topic of the review is the application of new ideas of unconventional quantum states to the physics of condensed matter, in particular of solid state, in the context of modern field theory. A comparison is made with classical papers on many-electron theory, including the formalism of many-electron operators. The essentially many-particle nature of the ground state, individual and collective excitations, and quantum fluctuations in the systems under consideration, as well as quantum phase transitions are discussed with an emphasis on topological aspects and with allowance for the effects of frustration. Variational approaches and representations of auxiliary particles, corresponding mean-field approximation and gauge field theory, confinement-deconfinement problem, violation of the Fermi-liquid picture, and exotic non-Fermi-liquid states are considered. An overview is given of the modern theory of entangled topological states, formation of spin liquid, strings and string networks.

Domain Wall Solitons Arising in Classical Gauge Field Theories

Domain wall solitons are basic constructs realizing phase transitions in various field-theoretical models and are solutions to some nonlinear ordinary differential equations descending from the corresponding full sets of governing equations in higher dimensions. In this paper, we present a series of domain wall solitons arising in several classical gauge field theory models. In the context of the Abelian gauge field theory, we unveil the surprising result that the solutions may explicitly be constructed, which enriches our knowledge on integrability of the planar Liouville type equations in their one-dimensional limits. In the context of the non-Abelian gauge field theory, we obtain some existence theorems for domain wall solutions arising in the electroweak type theories by developing some methods of calculus of variations formulated as direct and constrained minimization problems over a weighted Sobolev space.

Non-perturbative β-functions via Feynman graphons

We show the existence of a new class of [Formula: see text]-functions which can govern the running of strong coupling constants in gauge field theories.

Gauge PDE and AKSZ‐type Sigma Models

AbstractA gauge PDE is a natural notion which arises by abstracting what physicists call a local gauge field theory defined in terms of BV‐BRST differential (not necessarily Lagrangian). We study supergeometry of gauge PDEs paying particular attention to globally well‐defined definitions and equivalences of such objects. We demonstrate that a natural geometrical language to work with gauge PDEs is that of Q‐bundles. In particular, we demonstrate that any gauge PDE can be embedded into a super‐jet bundle of the Q‐bundle. This gives a globally well‐defined version of the so‐called parent formulation. In the case of reparameterization‐invariant systems, the parent formulation takes the form of an AKSZ‐type sigma model with an infinite‐dimensional target space.

Gauge invariance and the Englert-Brout-Higgs mechanism in non-Hermitian field theories

We discuss $\mathcal{P}\mathcal{T}$-symmetric Abelian gauge field theories as well as their extension to the Englert-Brout-Higgs mechanism for generating a mass for a vector boson. Gauge invariance is not straightforward, and we discuss the different related problems as well as a solution which consists in coupling the gauge field to a current that is not conserved. Non-Hermiticity then necessarily precludes the Lorenz gauge condition but nevertheless allows for a consistent formulation of the theory. We therefore generalize the Englert-Brout-Higgs mechanism to $\mathcal{P}\mathcal{T}$-symmetric field theories, opening the way to constructing non-Hermitian extensions of the Standard Model and new scenarios for particle model building.

Description of glass transition kinetics in 3D [formula omitted] model in terms of gauge field theory

A gauge theory of the glass transition in the frustrated XY model being simplest model containing topologically nontrivial excitations is considered. Investigation of the transition kinetics of this system finds that the three-dimensional system exhibits the Vogel–Fulcher–Tammann criticality going with its freezing into a spin glass. It is analytically shown that the system demonstrates all glass transition properties, like the logarithmic relaxation, and corresponding behaviour of linear and non-linear susceptibility. The mode-coupling theory equation in the Zwanziger–Mori representation also is derived in framework of our approach. The findings provide insights into the topological origin of glass formation, that allows to make progress in understanding glass-transition processes in more intricate systems.

Covariant Canonical Gauge Gravitation and Cosmology

The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations necessarily embrace a quadratic Riemann term added to Einstein’s linear equation. The quadratic term endows space-time with inertia generating a dynamic response of the space-time geometry to deformations relative to (Anti) de Sitter geometry. A “deformation parameter” is identified, the inverse dimensionless coupling constant governing the relative strength of the quadratic invariant in the Hamiltonian, and directly observable via the deceleration parameter q0. The quadratic invariant makes the system inconsistent with Einstein’s constant cosmological term, Λ = const. In the Friedman model this inconsistency is resolved with the scaling ansatz of a “cosmological function”, Λ(a), where a is the scale parameter of the FLRW metric. The cosmological function can be normalized such that with the A CDM parameter set the present-day observables, the Hubble constant and the deceleration parameter, can be reproduced. With this parameter set we recover the dark energy scenario in the late epoch. The proof that inflation in the early phase is caused by the “geometrical fluid” representing the inertia of space-time is yet pending, though. Nevertheless, as according to the CCGG theory the present-day cosmological function, identified with the currently observed Λobs, is a balanced mix of two contributions. These are the (A)dS curvature plus the residual vacuum energy of space-time and matter. The curvature term is proportional to the deformation parameter given by the coupling strength of the quadratic Riemann term. This allows for a fresh look at the Cosmological Constant Problem that plagues the standard Einstein-Friedman cosmology.

Gauge field theories with Lorentz-violating operators of arbitrary dimension

The classification of Lorentz- and CPT-violating operators in nonabelian gauge field theories is performed. We construct all gauge-invariant terms describing propagation and interaction in the action for fermions and gauge fields. Restrictions to the abelian, Lorentz-invariant, and isotropic limits are presented. We provide two illustrative applications of the results to quantum electrodynamics and quantum chromodynamics. First constraints on nonlinear Lorentz-violating effects in electrodynamics are obtained using data from experiments on photon-photon scattering, and corrections from nonminimal Lorentz and CPT violation to the cross section for deep inelastic scattering are derived.

Local Lorentz invariance and a new theory of gravitation equivalent to general relativity

A gauge theory of the Lorentz group with a mass-dimension one gauge field coupling to matter of any spin is developed. As a completely new feature the ‘Vierbein’ assuring local gauge invariance enters not as an independent dynamical field, but emerges as a functional of the Lorentz gauge field. The underlying geometry of the theory turns out to be a SO(1,3) Banach bundle. The most general action which is renormalizable by power-counting is constructed in terms of the gauge field and its first derivatives. It contains no higher derivative terms in the gauge field which destroy unitarity in the usual renormalizable R2-theories of gravitation. Finally equivalence of the Lorentz gauge field theory coupled to spin zero matter with general relativity is established.

Introdução à Teoria de Gauge da Gravitação

The fundamental interactions of nature, the electroweak and the quantum chromodynamics, are described in the Standard Model by the Gauge Theory under internal symmetries that maintain the invariance of the functional action. The fundamental interaction of gravitation is very well described by Einstein's General Relativity in a Riemannian spacetime metric, but General Relativity has been over time a gravitational field theory apart from the Standard Model. The theory of Gauge allows under symmetries of the group of Poincar\'e to impose invariances in the functional of the action of the spinor field that result in the gravitational interaction with the fermions. In this approach the gravitational field, besides being described by the equation similar to General Relativity, also brings a spin-gravitational interaction in a Riemann-Cartan spacetime.

The breaking of the SO(p, q) symmetry group to SO(p, q − n) × O(n) subjected to boundary conditions and its physical consequences for a gauge field theory

The consequences of imposing boundary conditions to extra spacetime coordinates on a gauge field theory are considered. In a toy model, a larger spacetime symmetry described by a Lorentz-Poincaré SO(p, q) group is broken to a symmetry group of the form due to boundary conditions in the extra dimensions, leading to an effectively massive gauge field coupled to a “scalar” field in the observable spacetime coordinates.

Canonical transformation path to gauge theories of gravity-II: Space-time coupling of spin-0 and spin-1 particle fields

The generic form of space-time dynamics as a classical gauge field theory has recently been derived, based on only the action principle and on the principle of general relativity. It was thus shown that Einstein’s general relativity is the special case where (i) the Hilbert Lagrangian (essentially the Ricci scalar) is supposed to describe the dynamics of the “free” (uncoupled) gravitational field, and (ii) the energy–momentum tensor is that of scalar fields representing real or complex structureless (spin-[Formula: see text]) particles. It followed that all other source fields — such as vector fields representing massive and nonmassive spin-[Formula: see text] particles — need careful scrutiny of the appropriate source tensor. This is the subject of our actual paper: we discuss in detail the coupling of the gravitational field with (i) a massive complex scalar field, (ii) a massive real vector field, and (iii) a massless vector field. We show that different couplings emerge for massive and nonmassive vector fields. The massive vector field has the canonical energy–momentum tensor as the appropriate source term — which embraces also the energy density furnished by the internal spin. In this case, the vector fields are shown to generate a torsion of space-time. In contrast, the system of a massless and charged vector field is associated with the metric (Hilbert) energy–momentum tensor due to its additional [Formula: see text] symmetry. Moreover, such vector fields do not generate a torsion of space-time. The respective sources of gravitation apply for all models of the dynamics of the “free” (uncoupled) gravitational field — which do not follow from the gauge formalism but must be specified based on separate physical reasoning.

Physics architecture. Part two

Physics architecture. Part two. The talk is devoted to the jubilee of academician M.A. Markov, who was born in 1908. Now we have also the 100th anniversary of the gauge invariance principle proposed by Weyl in 1918. During the period from 1967 to 1988 M.A. Markov was Academician Secretary of Nuclear Physics Department of AN USSR. He organized the series of conferences dedicated to the topical problems of theoretical, nuclear and elementary particle physics. One of them was international seminar “Vector mesons and electromagnetic interactions” under A.M. Baldin direct leadership. It went off in JINR in September of 1969. This very that seminar gave birth to the conferences series named “Baldin autumn”. Thanks to the discussions at the A.M. Baldin seminar many critical situations in theoretical and experimental physics were subsequently settled. The first plenary session of the seminar included L.D. Faddeev talk about gauge field quantization, which cleared the way to develop the renormalized quantum gauge field theory. My talk was dedicated to the transformation of the classical gauge field theory into geometrical one. As a result the unified geometrical theory was obtained, which could include any interactions together with Einsteinian gravity. In this connection both formulations of Weyl’s local gauge invariance principle (of 1918 and 1929) as well as Einsteinian principle of general relativity were used. This approach was based on the fibre bundle geometry, which was developed by mathematicians at that time. This theory gives a realizable classification of interactions according to the local Lie’s symmetry groups associated with them. This approach leads to the VIth Hilbert’s problem solution. To obtain further development of the gauge field theory, it is necessary to decide the question of the gauge field mass origin. It is the key moment both in quantum and geometrical classical theories of the gauge fields. Therefore it is very important to analyze the experiments, where massive and massless particles are converted in each other (similar Baldin experiments in JINR in 1967).

New multisymplectic approach to the Metric-Affine (Einstein-Palatini) action for gravity

We present a covariant multisymplectic formulation for the Einstein-Palatini (or Metric-Affine) model of General Relativity (without energy-matter sources). As it is described by a first-order affine Lagrangian (in the derivatives of the fields), it is singular and, hence, this is a gauge field theory with constraints. These constraints are obtained after applying a constraint algorithm to the field equations, both in the Lagrangian and the Hamiltonian formalisms. In order to do this, the covariant field equations must be written in a suitable geometrical way, using integrable distributions which are represented by multivector fields of a certain type. We obtain and explain the geometrical and physical meaning of the Lagrangian constraints and we construct the multimomentum (covariant) Hamiltonian formalism. The gauge symmetries of the model are discussed in both formalisms and, from them, the equivalence with the Einstein-Hilbert model is established.

Classical double copy: Kerr-Schild-Kundt metrics from Yang-Mills theory

The classical double copy idea relates some solutions of Einstein's theory with those of gauge and scalar field theories. We study the Kerr-Schild-Kundt (KSK) class of metrics in $d$-dimensions in the context of possible new examples of this idea. We first show that it is possible to solve the Einstein-Yang-Mills system exactly using the solutions of a Klein-Gordon type scalar equation when the metric is the $pp$-wave metric which is the simplest member of the KSK class. In the more general KSK class, the solutions of a scalar equation also solve the Yang-Mills, Maxwell and Einstein-Yang-Mills-Maxwell equations exactly albeit with a null fluid source. Hence in the general KSK class, the double copy correspondence is not as clean-cut as in the case of the $pp$-wave. In our treatment all the gauge fields couple to dynamical gravity, and are not treated as test fields. We also briefly study G\"{o}del type metrics along the same lines.

Stable, finite energy density solutions in the effective theory of non-abelian gauge fields

We consider the gauge fixed partition function of pure SU(Nc) gauge theory in axial gauge following the field strength formalism. We integrate over 3(Nc2−1) field strengths using the Bianchi identities and obtain an effective action of the remaining 3(Nc2−1) field strengths in momentum space. We obtain the static solutions of the equations of motion (EOM) of the effective theory. The solutions exhibit Gaussian nature in the z component of momentum and are proportional to delta functions of the remaining components of momentum. The solutions render a stable, finite energy density in the strong coupling region and the parameters of the solutions are proportional to fourth root of the gluon condensate, which acts as a natural mass scale in the low energy phase of the theory.

Schwinger-Dyson equations in Coulomb gauge consistent with numerical simulation

In the present work we undertake a study of the Schwinger-Dyson equation (SDE) in the Euclidean formulation of local quantum gauge field theory, with Coulomb gauge condition $\partial_i A_i = 0$. We continue a previous study which kept only instantaneous terms in the SDE that are proportional to $\delta(t)$ in order to calculate the instantaneous part of the time component of the gluon propagator $D_{A_0 A_0}(t, R)$. We compare the results of that study with a numerical simulation of lattice gauge theory and find that the infrared critical exponents and related quantities agree to within 1\% to 3\%. This raises the question, "Why is the agreement so good, despite the systematic neglect of non-instantaneous terms?" We discovered the happy circumstance that all the non-instantaneous terms are in fact zero. They are forbidden by the symmetry of the local action in Coulomb gauge under time-dependent gauge transformations $g(t)$. This remnant gauge symmetry is not fixed by the Coulomb gauge condition. The numerical result of the present calculation is the same as in the previous study; the novelty is that we now demonstrate that all the non-instantaneous terms in the SDE vanish. We derive some elementary properties of propagators which are a consequence of the remnant gauge symmetry. In particular the time component of the gluon propagator is found to be purely instantaneous $D_{A_0 A_0}(t, R) = \delta(t) V(R)$, where $V(R)$ is the color-Coulomb potential. Our results support the simple physical scenario in which confinement is the result of a linearly rising color-Coulomb potential, $V(R) \sim \sigma R$ at large $R$.

Gauge method for a special spinor field transformation

In this paper, the gauge method for a special spinor field transformation Ψ(x) → Ψ′(x) = exp[(e/m)f(x)γa∂a]Ψ(x) is studied. We demonstrate that the Dirac equation involving electromagnetic interactions can be defined by the gauge method for the spinor field transformation, within the framework of gauge field theory.