Gauge-fixing Parameter Research Articles

Finite temperature reduction of the SU(2) Higgs model with complete static background

Direct evaluation of the 1-loop fluctuation determinant of non-static degrees of freedom in a complete static background is advocated to be more efficient for the determination of the effective three-dimensional model of the electroweak phase transition than the one-by-one evaluation of Feynman diagrams. The relation of the couplings and fields of the effective model to those of the four-dimensional finite temperature system is determined in the general 't Hooft gauge with full implementation of renormalisation effects. Only field renormalisation constants display dependence on the gauge fixing parameter. Characteristics of the electroweak transition are computed from the effective theory in Lorentz gauge. The dependence of various physical observables on the three-dimensional gauge fixing parameter is investigated.

Gauge fixing dependence of the one-loop divergences in higher-derivative quantum gravity with scalar field and the effective potential

The one-loop divergences in higher-derivative quantum gravity with scalar field are calculated with the use of a non-minimal two-parameter gauge fixing condition. The explicit gauge fixing parameter dependence of the effective potential is demonstrated. However, the one-loop function of the scalar coupling does not depend on the gauge fixing choice. This fact verifies the correctness of the function calculation. In the limiting case of the minimal gauge our results coincide with the renormalization group functions calculated in previous papers.

Structure of the effective potential in nonrelativistic Chern-Simons field theory.

We present the scalar field effective potential for nonrelativistic self-interacting scalar and fermion fields coupled to an Abelian Chern-Simons gauge field. Fermions are non-minimally coupled to the gauge field via a Pauli interaction. Gauss's law linearly relates the magnetic field to the matter field densities; hence, we also include radiative effects from the background gauge field. However, the scalar field effective potential is transparent to the presence of the background gauge field to leading order in the perturbative expansion. We compute the scalar field effective potential in two gauge families. We perform the calculation in a gauge reminiscent of the $R_\xi$-gauge in the limit $\xi\rightarrow 0$ and in the Coulomb family gauges. The scalar field effective potential is the same in both gauge-fixings and is independent of the gauge-fixing parameter in the Coulomb family gauge. The conformal symmetry is spontaneously broken except for two values of the coupling constant, one of which is the self-dual value. To leading order in the perturbative expansion, the structure of the classical potential is deeply distorted by radiative corrections and shows a stable minimum around the origin, which could be of interest when searching for vortex solutions. We regularize the theory with operator regularization and a cutoff to demonstrate that the results are independent of the regularization scheme.

NONPERTURBATIVE QUARK PROPAGATOR APPROACH TO QCD AT LARGE DISTANCES

A nonperturbative approach to QCD at large distances in the context of the Schwinger-Dyson equations and corresponding Slavnov-Taylor identity in the quark sector is presented. Making only one widely accepted assumption that the full gluon propagator becomes an infrared singular like (q2)−2 in the arbitrary covariant gauge, we find three and only three confinement-type solutions for the quark propagator (quark confinement theorem). Two of them vanish after the removal of the infrared regulation parameter. The third solution does not depend on this latter parameter, but it has no pole and it implies dynamical chiral symmetry breakdown (DCSB), which means a close connection between quark confinement and DCSB. We also show that multiplication solely by the quark infrared renormalization constant would make all the Green’s functions infrared finite (multiplicative renormalizability). The final forms of the renormalized (infrared finite) quark SD equations do not explicitly depend on a gauge-fixing parameter (“gauge invariance”). Our approach is free of ghost complications despite the fact that they play an essential role in nonperturbative dynamics. Our approach also implies the existence of a characteristic scale at which confinement, DCSB and other nonperturbative effects become essential. We solve explicitly the SD equation with corresponding ST identity for the above-mentioned IR finite quark propagator in the chiral limit and apply an effective potential in order to determine completely this solution.

Quantization of Yang-Mills theory without Gribov copies: Perturbative renormalization.

We calculate the one-loop correction to the gluon propagator for a pure Yang-Mills theory with a soft gauge fixing which avoids the problem of Gribov copies. It is found that the propagator reduces, in the limit in which the gauge-fixing parameter $M$ is taken to infinity, to the conventional one in the Landau gauge. The $M$-dependent propagator is then used to check that the gauge dependence disappears when calculating the vacuum expectation value (VEV) of gauge-invariant observables. These two facts are used to discuss how finite results might be obtained, beyond the tree level, for VEV's of gauge-invariant observables.

Gauge independence in Hadamard renormalization.

We examine the dependence of the Hadamard-renormalized stress-energy tensor on the gauge-fixing parameter for electromagnetism and one-loop gravity. Simple arguments show that the stress-energy tensor is independent of the parameter.

Hot gluon matter in a constantA 0 background

We compute the effective action of finiteT SU(3) gauge theory in a constant diagonal background fieldA 0(t,x)=B 0 3 T3+B 0 8 T8 in the general covariant background gauge up to terms of orderg 3.B 0 3,8 shield the infrared singularities and the aim is to study whether the minimum of the effective action would determine their values dynamically. We find that the orderg 2 term depends explicitly on the gauge fixing parameter ξ. Since the background field screens already at the tree diagram level the interactions of the six non-diagonal gluon fields they do not contribute to the plasmon-likeg 3 term. The two diagonal fieldsA 0 3 ,A 0 8 do, but the electric mass squared they develop will become negative if the background fields are larger than aboutT/g. Hence large background fields make the system unstable.

Effect of gauge fixing term in three dimensional stationary magnetic fields problem

Gauge fixing in 3-D stationary linear magnetic fields in a finite volume is achieved under some particular assumptions. Divergence of inner region A satisfies the Laplace equation by using a conventional gauge-fixing term to the gauge-invariant Lagrangian. Taking into account the assumed zero boundary condition for divA on the natural boundary condition surface, it is found that divA vanishes all over the region theoretically. Uniqueness of the solution is proved in another particular case. A numerical analysis is presented and the optimal value of the gauge-fixing parameter alpha is examined. >

Stochastic quantization of Yang-Mills field theory: Gauge-fixing parameter dependence and equilibrium limit.

We calculate, in the framework of stochastic quantization, the one-loop-divergent part of the gluon self-energy and the triple-gluon vertex of pure Yang-Mills field theory, with an arbitrary choice of the stochastic gauge-fixing parameter. This allows us to check that the strong conditions imposed by renormalizability are satisfied up to one-loop order. We compare our results with those coming from the Faddeev-Popov theory and discuss the relationship between both approaches in the equilibrium limit.

Integral-spin fields on (3+2)-de Sitter space

Nowadays, (3+2)-de Sitter (or anti-de Sitter space) appears as a very attractive possibility at several levels of theoretical physics. The Wigner definition of an elementary system as associated to a unitary irreducible representation of the Poincaré group may be extended to the de Sitter group SO(3,2) [or ∼(SO(3,2))] without great difficulty. The constant curvature, as small as it can be, is a natural candidate to play the role of a regularization parameter with respect to the flat-space limit. Massless particles in (3+2)-de Sitter theory are composite (singletons). On the other hand, supergravity theories necessitate a (large) constant curvature. The content of this paper is group theoretical. It attempts to continue the ‘‘à la Wigner’’ program for SO(3,2), already largely broached by Fronsdal. Three recurrence formulas are presented. They permit one to build up the carrier states for representations with arbitrary integral spin. Two of them are valid for the ‘‘massive’’ representations whereas the third one is applicable to the indecomposable massless representations. In addition, other presumably indecomposable, though nonphysical, representations are studied, in relation to the existence of ‘‘generalized’’ gauge fields and divergences. The recurrence formulas also allow one to build up the invariant two-point functions or homogeneous propagators. Hence it becomes possible to examine the problems of light-cone propagation and ‘‘reverberation’’ into the light cone and to make the following assertion: for a certain choice of the gauge-fixing parameters, the massless states with arbitrary spin propagate only on the light cone and whatever gauge one chooses their physical parts propagate on the light cone.

Gauge-dependence of self-consistent dimensional reduction

The use of the quantum gravity one-loop effective potential to self-consistently determine the radius of the compact dimension in M 4 × S 1 Kaluza-Klein theory is critically examined. It is explicitly demonstrated that the predicted radius, as well as physical parameters of the effective four-dimensional theory, depend on the value of the gauge-fixing parameter chosen to carry out the calculations.

Gauge fixing and massless, integral-spin fields in de sitter space

The classical field theories of massless fields of arbitrary, fixed, integral spins reach their simplest Gupta-Bleuler triplet structure when the gauge-fixing parameter c is put equal to zero (‘the Feynman Gauge’). This value of c is peculiar to the flat space theory. In a De Sitter massless field theory with spin s, the ‘best value’ of c is shown to be equal to 2/2s+1.

Neutrino charge in the linearRξgauge

It is shown that in the $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ model of electroweak interactions dimensional regularization guarantees the vanishing of the one-loop contributions to the neutrino charge for every dimension $n$ and for every value of the gauge-fixing parameter $\ensuremath{\xi}$ without the need for counterterms and without having to invoke Ward identities.

Solution of the renormalization group equation and ultraviolet asymptotics of gauge-dependent propagators in QCD

The general solution of the RGE for gluon vertices in massless QCD is obtained for arbitrary α. It is shown that, contrary to the view prevailing in the literature, the ultraviolet behaviour of gluon vertices is discontinuous both in the gauge-fixing parameter α and in the number of flavours.

Locally gauge-invariant charged states in quantum electrodynamics

In a covariant formulation of spinor electrodynamics a la Hertz it is possible to introduce electrically charged matter fields and a vector potential which are invariant under local gauge transformations (characterized by functions vanishing at infinity). The connected Green’s functions relative to such fields turn out to not depend on the gaugefixing parameter and coincide with the corresponding Green’s functions of usual quantum electrodynamics, evaluated in the Landau (fourdimensional transversal) gauge. The states obtained by applying these fields on the vacuum are, however, nonphysical,i.e. Maxwell equations are not weakly satisfied on them. In other words, in the Hertz formulation of quantum electrodynamics local gauge invariance does not imply physicity. Also explicit examples are given of locally gauge-invariant charged physical fields, which are nonlocal with respect to the electromagnetic field.

A stagnant gauge for QCD

It is shown that the gauge-fixing parameter α of standard covariant gauges may legitimately be replaced by an operator α(□). In particular, α may be chosen so that the gluon propagator has a “stagnant” tensor structure proportional to g ην for all momenta. This choice of gauge simplifies explicit calculations and leads to renormalization group equations with no ∂ ∂α term.

Supersymmetric quantization of linearized supergravity

We give a manifestly supersymmetric quantization scheme for linearized supergravity, motivated by the desire to develop a background field method for the full non-linear theory. Supersymmetric gauge-fixing constraints are constructed and the corresponding ghost action is discussed. It is found that the Faddeev-Popov action itself possesses invariances, requiring “secondary” gauge fixing, which in turn leads to “secondary” ghost fields, the latter having normal statistics. The gauge-fixing constraints are used to construct gauge-fixing terms in the action, with a total of four gauge-fixing parameters. The superpropagators are found and may be greatly simplified by certain choices of these parameters.