Classical Gauge Field Research Articles

Rare interactions of neutrinos with matter as contraction of the Electroweak Model

The modification of the electroweak model with contracted gauge group SU(2; ϵ) × U(1) is suggested. The field space of the model is fibered under contraction in such a way that neutrino fields are in the fiber. Properties of the fibered field space are understood in context of semi-Riemannian geometry. Contraction of gauge group is connected with the limit properties of the cross-section for interactions of neutrinos with matter, when neutrinos energy tends to zero. For small contraction parameter this model explain already at the level of classical gauge fields why neutrinos so rarely interact with anything and why their cross-section with matter increase with energy. Small contraction parameter is connected with the universal Fermi constant of weak interactions and neutrino energy as The modified model need be considered at low energies much less then gauge bosons masses.

On the Description of Motion of a Quantum Particle in the Classical Gauge Field in the Language of Stochastic Mechanics

An equation of Newton–Nelson type on the vector bundle over space-time of General Relativity is introduced and investigated. The equation is interpreted as the one describing the motion of a quantum particle in the classical gauge field in the language of stochastic mechanics.

Electrically and magnetically charged vortices in the Chern–Simons–Higgs theory

In this paper, we prove the existence of finite-energy electrically and magnetically charged vortex solutions in the full Chern–Simons–Higgs theory, for which both the Maxwell term and the Chern–Simons term are present in the Lagrangian density. We consider both Abelian and non-Abelian cases. The solutions are smooth and satisfy natural boundary conditions. Existence is established via a constrained minimization procedure applied on indefinite action functionals. This work settles a long-standing open problem concerning the existence of dually charged vortices in the classical gauge field Higgs model minimally extended to contain a Chern–Simons term.

Non-Abelian Optical Lattices: Anomalous Quantum Hall Effect and Dirac Fermions

We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electrodynamics, offering a remarkable route to access the exotic properties of massless Dirac fermions with cold atoms experiments. In particular, we show that the underlying Minkowski space-time can also be modified, reaching anisotropic regimes where a remarkable anomalous quantum Hall effect and a squeezed Landau vacuum could be observed.

Proof of the Julia–Zee Theorem

It is a well accepted principle that finite-energy static solutions in the classical relativistic gauge field theory over the (2 + 1)-dimensional Minkowski spacetime must be electrically neutral. We call such a statement the Julia–Zee theorem. In this paper, we present a mathematical proof of this fundamental structural property.

Classical initial conditions in high energy nucleus-nucleus collisions

An iterative proceedure is proposed to compute the classical gauge field produced in the collision of two heavy nuclei. The leading order is obtained by linearizing the Yang-Mills equations in the light-cone gauge, and provides a simple formula for gluon production in nucleus-nucleus collisions. At this order k t –factorization breaks down.

Lectures on Classical Integrable Systems and Gauge Field Theories

In these lectures we consider Hitchin integrable systems and their relations with the self-duality equations and twisted super-symmetric Yang-Mills theory in four dimension. We define the Symplectic Hecke correspondence between different integrable systems. As an example we consider Elliptic Calogero-Moser system and integrable Euler-Arnold top on coadjoint orbits of the group GL(N, C) and explain the Symplectic Hecke correspondence for these systems.

Green functions for wave propagation on a five-dimensional manifold and the associated gauge fields generated by a uniformly moving point source

Gauge fields associated with the manifestly covariant dynamics of particles in (3,1) space time are five dimensional (5D). We provide solutions of the classical 5D gauge field equations in both (4,1) and (3,2) flat space-time metrics for the simple example of a uniformly moving point source. Green functions for the 5D field equations are obtained, which are consistent with the solutions for uniform motion obtained directly from the field equations with free asymptotic conditions.

Slowly decaying classical fields, unitarity, and gauge invariance

In classical external gauge fields that fall off less fast than the inverse of the evolution parameter (time) of the system the implementability of a unitary perturbative scattering operator ($S$-matrix) is not guaranteed, although the field goes to zero. The importance of this point is exposed for the counterexample of low-dimensionally expanding systems. The issues of gauge invariance and of the interpretation of the evolution at intermediate times are also intricately linked to that point.

Higher derivatives and brane-localised kinetic terms in gauge theories on orbifolds

We perform a detailed analysis of one-loop corrections to the self-energy of the (off-shell) gauge bosons in six-dimensional N=1 supersymmetric gauge theories on orbifolds. After discussing the Abelian case in the standard Feynman diagram approach, we extend the analysis to the non-Abelian case by employing the method of an orbifold-compatible one-loop effective action for a classical background gauge field. We find that bulk higher derivative and brane-localised gauge kinetic terms are required to cancel one-loop divergences of the gauge boson self energy. After their renormalisation we study the momentum dependence of both the higher derivative coupling h(k^2) and the {\it effective} gauge coupling g_eff(k^2). For momenta smaller than the compactification scales, we obtain the 4D logarithmic running of g_eff(k^2), with suppressed power-like corrections, while the higher derivative coupling is constant. We present in detail the threshold corrections to the low energy gauge coupling, due to the massive bulk modes. At momentum scales above the compactification scales, the higher derivative operator becomes important and leads to a power-like running of g_eff(k^2) with respect to the momentum scale. The coefficient of this running is at all scales equal to the renormalised coupling of the higher derivative operator which ensures the quantum consistency of the model. We discuss the relation to the similar one-loop correction in the heterotic string, to show that the higher derivative operators are relevant in that case too, since the field theory limit of the one-loop string correction does not commute with the infrared regularisation of the (on-shell) string result.

Hamiltonian equations of gluonic lattice gauge fields in the continuum limit

We study classical gluonic lattice gauge fields in the Hamiltonian approach, using a Hamiltonian function that resembles the lattice Hamiltonian of Kogut and Susskind. We derive the equations of motion and show that they pass to the field equations in the continuum limit.

Projective geometry and special relativity

In this paper we present the Koopman-von Neumann (KvN) formulation of classical non-Abelian gauge field theories. In particular we shall explore the functional (or classical path integral) counterpart of the KvN method. In the quantum path integral quantization of Yang-Mills theories concepts like gauge-fixing and Faddeev-Popov determinant appear in a quite natural way. We will prove that these same objects are needed also in this classical path integral formulation for Yang-Mills theories. We shall also explore the classical path integral counterpart of the BFV formalism and build all the associated universal and gauge charges. These last are quite different from the analog quantum ones and we shall show the relation between the two. This paper lays the foundation of this formalism which, due to the many auxiliary fields present, is rather heavy. Applications to specific topics outlined in the paper will appear in later publications.

D-theory: field quantization by dimensional reduction of discrete variables

D-theory is an alternative non-perturbative approach to quantum field theory formulated in terms of discrete quantized variables instead of classical fields. Classical scalar fields are replaced by generalized quantum spins and classical gauge fields are replaced by quantum links. The classical fields of a d-dimensional quantum field theory reappear as low-energy effective degrees of freedom of the discrete variables, provided the ( d+1)-dimensional D-theory is massless. When the extent of the extra Euclidean dimension becomes small in units of the correlation length, an ordinary d-dimensional quantum field theory emerges by dimensional reduction. The D-theory formulation of scalar field theories with various global symmetries and of gauge theories with various gauge groups is constructed explicitly and the mechanism of dimensional reduction is investigated.

Fermion production in time-dependent fields

The exact fermion propagator in a classical time-dependent gauge field is derived by solving the equation of motion for the Dirac Green's functions. From the retarded propagator obtained in this way the momentum spectrum for the produced fermion pairs is calculated. Different approximations and the exact solution for the propagator and the momentum spectrum are presented.

On anomalies in orbifold theories

We study the issue of gauge invariance in five-dimensional theories compactified on an orbifold S1/(Z2×Z′2) in the presence of an external U(1) gauge field. From the four-dimensional point of view the theory contains a tower of Kaluza–Klein Dirac fermions with chiral couplings and it looks anomalous at the quantum level. We show that this “anomaly” is cancelled by a topological Chern–Simons term which is generated in the effective action when the gauge theory is regularized introducing a Pauli–Villars fermion with an odd mass term. In the presence of a classical background gauge field, the fermionic current acquires a vacuum expectation value, thus generating the suitable Chern–Simons term and a gauge invariant theory.

Resonant amplification of electroweak baryogenesis at preheating

We explore viable scenarios for parametric resonant amplification of electroweak (EW) gauge fields and the Chern-Simons number during preheating, leading to baryogenesis at the EW scale. In this class of scenarios time-dependent classical EW gauge fields, essentially spatially homogeneous on the horizon scales, carry the Chern-Simons number which can be amplified by parametric resonance up to magnitudes at which unsuppressed topological transitions in the Higgs sector become possible. Baryon number nonconservation associated with the gauge sector and the highly non-equilibrium nature of preheating allow for efficient baryogenesis. The requisite large $\mathrm{CP}$ violation can arise either from the time dependence of a slowly varying Higgs field (spontaneous baryogenesis) or from a resonant amplification of $\mathrm{CP}$ violation induced in the gauge sector through loops. We identify several $\mathrm{CP}$-violating operators in the standard model and its minimal extensions that can facilitate efficient baryogenesis at preheating, and we show how to overcome would-be exponential suppression of baryogenesis associated with tunneling barriers.

The Mathematical Role of Time and Space-Time in Classical Physics

We use Padoa's principle of independence of primitive symbols in axiomatic systems in order to discuss the mathematical role of time and spacetime in some classical physical theories. We show that time is eliminable in Newtonian mechanics and that spacetime is also dispensable in Hamiltonian mechanics, Maxwell's electromagnetic theory, the Dirac electron, classical gauge fields, and general relativity.

Real-time dynamics in the 1+1 D abelian Higgs model with fermions

In approximate dynamical equations, inhomogenous classical (mean) gauge and Higgs fields are coupled to quantized fermions. The equations are solved numerically on a spacetime lattice. The fermions appear to equilibrate according to the Fermi-Dirac distribution with time-dependent temperature and chemical potential.

Exact solutions of classical electrodynamics and the Yang-Mills-Wong theory in even-dimensional space-time

Exact solutions of classical gauge theories in even-dimensional (D=2n) space-time are discussed. Common and specific properties of these solutions are analyzed for the particular dimensions D=2, D=4, and D=6. The consistent formulation of classical gauge field theories with pointlike charged or colored particles is proposed for D=6. The particle Lagrangian must then depend on the acceleration. In D=2, radiation is absent and all processes are invertible w.r.t. time. In D=6, the expression for the radiation intensity, as well as the equation of motion of a self-interacting particle, is obtained; trembling always leads to radiation. Non-Abelian solutions are absent for any D≠4, and only Coulomb-like solutions, which correspond to the Abelian limit of the D-dimensional Yang-Mills-Wong theory, are admitted.

Quantum spins and quantum links: The D-theory approach to field theory

A new non-perturbative approach to quantum field theory is proposed. Instead of performing a path integral over configurations of classical fields, D-theory works with discrete quantized variables. Classical spin fields are replaced by quantum spins, and classical gauge fields are replaced by quantum links. The classical fields of a d-dimensional quantum field theory reappear as low-energy effective degrees of freedom of the discrete variables, provided the ( d+1)-dimensional D-theory is massless. When the extent of the extra Euclidean dimension becomes small in units of the correlation length, an ordinary d-dimensional quantum field theory emerges by dimensional reduction. The D-theory formulation of some spin models and gauge theories is constructed explicitly. In particular, QCD emerges as a quantum link model.