Gauge-fixing Approach Research Articles

Modified Nonlinear Model of Arcsin-Electrodynamics

A new modified model of nonlinear arcsin-electrodynamics with two parameters is proposed and analyzed. We obtain the corrections to the Coulomb law. The effect of vacuum birefringence takes place when the external constant magnetic field is present. We calculate indices of refraction for two perpendicular polarizations of electromagnetic waves and estimate bounds on the parameter γ from the BMV and PVLAS experiments. It is shown that the electric field of a point-like charge is finite at the origin. We calculate the finite static electric energy of point-like particles and demonstrate that the electron mass can have the pure electromagnetic nature. The symmetrical Belinfante energy-momentum tensor and dilatation current are found. We show that the dilatation symmetry and dual symmetry are broken in the model suggested. We have investigated the gauge covariant quantization of the nonlinear electrodynamics fields as well as the gauge fixing approach based on Dirac's brackets.

Tensor gauge condition and tensor field decomposition

We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin [Formula: see text]. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.

Gauge fixing, BRS invariance and Ward identities for randomly stirred flows

The Galilean invariance of the Navier–Stokes equation is shown to be akin to a global gauge symmetry familiar from quantum field theory. This symmetry leads to a multiple counting of infinitely many inertial reference frames in the path integral approach to randomly stirred fluids. This problem is solved by fixing the gauge, i.e., singling out one reference frame. The gauge fixed theory has an underlying Becchi–Rouet–Stora (BRS) symmetry which leads to the Ward identity relating the exact inverse response and vertex functions. This identification of Galilean invariance as a gauge symmetry is explored in detail, for different gauge choices and by performing a rigorous examination of a discretized version of the theory. The Navier–Stokes equation is also invariant under arbitrary rectilinear frame accelerations, known as extended Galilean invariance (EGI). We gauge fix this extended symmetry and derive the generalized Ward identity that follows from the BRS invariance of the gauge-fixed theory. This new Ward identity reduces to the standard one in the limit of zero acceleration. This gauge-fixing approach unambiguously shows that Galilean invariance and EGI constrain only the zero mode of the vertex but none of the higher wavenumber modes.

PJLZ gauge-fixing approach in SU(2) lattice gauge theory

We study the SU(2) gauge theory with the interpolating gauge {\it a la} Parrinello--Jona-Lasinio--Zwanziger (PJLZ) with the gauge fixing functional $F=\sum_{x\mu} {1/2}\tr (U_{x\mu}\sigma_3U_{x\mu}^{\dagger}\sigma_3)$. We find a strong indication of the non--analiticity with respect to the interpolating parameter $\lambda$ at $\lambda_c \sim 0.8$.

Nonperturbative gauge fixing and perturbation theory

We compare the gauge-fixing approach proposed by Jona-Lasinio and Parrinello, and by Zwanziger (JPLZ) with the standard Fadeev-Popov procedure, and demonstrate perturbative equality of gauge-invariant quantities, up to irrelevant terms induced by the cutoff. We also show how a set of local, renormalizable Feynman rules can be constructed for the JPLZ procedure.

New tests of the gauge-fixing approach to lattice chiral gauge theories

We report on recent progress with the gauge-fixing approach to lattice chiral gauge theories. The bosonic sector of the gauge-fixing approach is studied with fully dynamical U(1) gauge fields. We demonstrate that it is important to formulate the Lorentz gauge-fixing action such that the dense set of lattice Gribov copies is removed, and the gauge-fixing action has a unique absolute minimum. We then show that the spectrum in the continuum limit contains only the desired massless photon, as expected.

New tests of the gauge-fixing approach to lattice chiral gauge theories

New tests of the gauge-fixing approach to lattice chiral gauge theories

More on lattice BRST invariance

In the gauge-fixing approach to (chiral) lattice gauge theories, the action in the U(1) case implicitly contains a free ghost term, in accordance with the continuum abelian theory. On the lattice there is no BRST symmetry and, without fermions, the partition function is strictly positive. Recently, Neuberger pointed out in hep-lat/9801029 that a different choice of the ghost term would lead to a BRST-invariant lattice model, which is ill-defined nonperturbatively. We show that such a lattice model is inconsistent already in perturbation theory, and clearly different from the gauge-fixing approach.

Phase diagram of a lattice U(1) gauge theory with gauge fixing

As a first step towards a nonperturbative investigation of the gauge-fixing (Rome) approach to lattice chiral gauge theories we study a U(1) model with an action that includes a local gauge-fixing term and a mass counterterm for the gauge fields. The model is studied on the trivial orbit so that only the dynamics of the longitudinal gauge degrees of freedom is taken into account. The phase diagram of this higher-derivative scalar field theory is determined, both in the mean-field approximation and numerically. The continuum limit of the model corresponds to a continuous phase transition between a ferromagnetic (FM) phase where the global U(1) symmetry is broken, and a so-called helicoidal ferromagnetic (FMD) phase with broken U(1) symmetry and a nonvanishing condensate of the vector field. The global U(1) symmetry is restored in this continuum limit. We show that our data for the magnetization in the FM and FMD phases are in good agreement with perturbation theory.

Chiral fermions on the lattice through gauge fixing: Perturbation theory

We study the gauge-fixing approach to the construction of lattice chiral gauge theories in one-loop weak-coupling perturbation theory. We show how the infrared properties of the gauge degrees of freedom determine the nature of the continuous phase transition at which we take the continuum limit. The fermion self-energy and the vacuum polarization are calculated, and confirm that, in the Abelian case, this approach can be used to put chiral gauge theories on the lattice in four dimensions. We comment on the generalization to the non-Abelian case.

Gauge-fixing approach to lattice chiral gauge theories, part II

In this more technical part we give additional details on the gauge-fixing approach [1,2] presented in [3]. We also explain how the gauge-fixing approach evades the Nielsen-Ninomiya [4] no-go theorem.

Gauge-fixing approach to lattice chiral gauge theories

We report on recent progress with the definition of lattice chiral gauge theories, using a lattice action that includes a discretized Lorentz gauge-fixing term. This gauge-fixing term has a unique global minimum, and allows us to use perturbation theory in order to study the influence of the gauge degrees of freedom on the fermions. For the abelian case, we find, both in perturbation theory and numerically, that the fermions remain chiral, and that there are no doublers.

The standard model from a new phase transition on the lattice

Several years ago it was conjectured in the so-called Roma Approach, that gauge fixing is an essential ingredient in the lattice formulation of chiral gauge theories. In this paper we discuss in detail how the gauge-fixing approach may be realized. As in the usual (gauge invariant) lattice formulation, the continuum limit corresponds to a gaussian fixed point, that now controls both the transversal and the longitudinal modes of the gauge field. A key role is played by a new phase transition separating a conventional Higgs or Higgs-confinement phase, from a phase with broken rotational invariance. In the continuum limit we expect to find a scaling region, where the lattice correlators reproduce the euclidean correlation functions of the target (chiral) gauge theory, in the corresponding continuum gauge.

Covariant gauges for constrained systems

The conventional Dirac gauge-fixing approach for degenerate theories is generalized with the aim to include covariant gauge conditions in the consideration. For this purpose a method to construct an extended phase space without Grassmann variables is proposed. For a given gauge depending on the velocities and accelerations up to order k, the extension of the phase space is carried out by rewriting the original theory in the form of a theory with higher-order derivatives (the highest order is k + 1) and applying to the latter the Ostrogradsky method of Hamiltonian description. As a result, the covariant gauge in extended phase space can be employed in the same manner as the unitary one.