Arbitrary Gauge Parameter Research Articles

Higgs scalar potential coupled to gravity in the exponential parametrization in arbitrary gauge

We study the parametrization and gauge dependences in the Higgs field coupled to gravity in the context of asymptotic safety. We use the exponential parametrization to derive the fixed points for the cosmological constant, Planck mass, Higgs mass and its coupling, keeping arbitrary gauge parameters $\ensuremath{\alpha}$ and $\ensuremath{\beta}$, and compare the results with the linear split. We find that the beta functions for the Higgs potential are expressed in terms of redefined Planck mass such that the apparent gauge dependence is absent. Only the trace mode of the gravity fluctuations couples to the Higgs potential and it tends to decouple in the large $\ensuremath{\beta}$ limit, but the anomalous dimension becomes large, invalidating the local potential approximation. This gives the limitation of the exponential parametrization. There are also singularities for some values of the gauge parameters but well away from these, we find rather stable fixed points and critical exponents. We thus find that there are regions for the gauge parameters to give stable fixed points and critical exponents against the change of gauge parameters. The Higgs coupling is confirmed to be irrelevant for the reasonable choice of gauge parameters.

Nonperturbative gluon pair production from a constant chromo-electric field via the Schwinger mechanism in arbitrary gauge

We study the non-perturbative production of gluon pairs from a constant SU(3) chromo-electric background field via the Schwinger mechanism. We fix the covariant background gauge with an arbitrary gauge parameter \alpha. We determine the transverse momentum distribution of the gluons, as well as the total probability of creating pairs per unit space time volume. We find that the result is independent of the covariant gauge parameter \alpha used to define arbitrary covariant background gauges. We find that our non-perturbative result is both gauge invariant and gauge parameter \alpha independent.

On the photon Green functions in curved spacetime

Quantization of electrodynamics in curved spacetime in the Lorentz gauge and with arbitrary gauge parameter makes it necessary to study Green functions of non-minimal operators with variable coefficients. Starting from the integral representation of photon Green functions, we link them to the evaluation of integrals involving Γ-functions. Eventually, the full asymptotic expansion of the Feynman photon Green function at small values of the world function, as well as its explicit dependence on the gauge parameter, are obtained without adding by hand a mass term to the Faddeev–Popov Lagrangian. Coincidence limits of the second covariant derivatives of the associated Hadamard function are also evaluated, as a first step towards the energy–momentum tensor in the non-minimal case.

Formula omitted] vs. pole masses of gauge bosons: electroweak bosonic two-loop corrections

The relationship between MS and pole masses of the vector bosons Z and W is calculated at the two-loop level in the Standard Model. We only consider the purely bosonic contributions which represent a gauge invariant subclass of diagrams. All calculations were performed in the linear R ξ gauge with three arbitrary gauge parameters utilizing the method of asymptotic expansions. The results are presented in analytic form as series in the small parameters sin 2 θ W and the mass ratio m Z 2/ m H 2. We also present the corresponding on-shell mass counter-terms for the massive gauge bosons, which will be needed for the calculation of observables at two-loops in the on-shell renormalization scheme.

QUANTIZATION OF MASSIVE ABELIAN ANTISYMMETRIC TENSOR FIELD AND LINEAR POTENTIAL

We discuss a quantum-theoretical aspect of the massive Abelian antisymmetric tensor gauge theory with antisymmetric tensor current. To this end, an Abelian rank-2 antisymmetric tensor field is quantized both in the covariant gauge with an arbitrary gauge parameter and in the axial gauge of the Landau type. The covariant quantization yields the generating functional written in terms of an antisymmetric tensor current and its divergence. Origins of the terms in the generating functional are clearly understood in comparison with the quantization in the unitary gauge. The quantization in the axial gauge with a suitable axis directly yields the generating functional which is the same as that obtained by using Zwanziger's formulation for electric and magnetic charges. It is shown that the generating functionals lead to a composite of the Yukawa and the linear potentials.

Nonlocal regularization and spontaneously broken abelian gauge theories for an arbitrary gauge parameter

We study the nonlocal regularization for the case of a spontaneously broken abelian gauge theory in the Rξ-gauge with an arbitrary gauge parameter ξ. We consider a simple abelian-Higgs model with chiral couplings as an example. We show that if we apply the nonlocal regularization procedure (to construct a nonlocal theory with FINITE mass parameter) to the spontaneously broken Rξ-gauge Lagrangian, using the quadratic forms as appearing in this Lagrangian, we find that a physical observable in this model, an analogue of the muon anomalous magnetic moment, evaluated to order O [g2] does indeed show ξ-dependence. We then apply the modified form of nonlocal regularization that was recently advanced and studied for the unbroken non-abelian gauge theories and discuss the resulting WT identities and ξ-independence of the S-matrix elements.

Gauge-independent thermal β function in Yang-Mills theory via the pinch technique

It is proposed to use the pinch technique to obtain the gauge-independent thermal β function β T in a hot Yang-Mills gas. Calculations of β T are shown detail at one-loop level in two different gauges, (i) the background field method with an arbitrary gauge parameter and (ii) the Coulomb gauge. When the pinch contributions to the gluon self-energy are included, the same result is derived for β T in both cases.

Green functions from a gauge-invariant effective action for the electroweak Standard Model

Application of the background-field method to the electroweak Standard-Model yields a gauge-invariant effective action giving rise to simple Ward identities. We find that in the backgroun-field 't Hooft-Feynman gauge the resulting vertex functions are exactly those that are obtained using the pinch technique. Thus, the background-field method provides a general framework that generalizes the pinch technique directly and uniquely to arbitrary Green functions and arbitrary orders of perturbation theory. Moreover, the desirable properties of the pinch-technique vertex functions hold for arbitrary gauge parameters and have a simple explanation within the background-field method.

Gauge invariance of Green functions: background-field method versus pinch technique

Application of the background-field method to QCD and the electroweak Standard Model yields gauge-invariant effective actions giving rise to simple Ward identities. Within this method, we calculate the quantities that have been treated in the literature using the pinch technique. Putting the quantum gauge parameter equal to one, we recover the pinch-technique results as a special case of the background-field method. The one-particle-irreducible Green functions of the background-field method fulfil for arbitrary gauge parameters the desirable theoretical properties that have been noticed within the pinch technique. Therefore the background-field formalism provides a general framework for the direct calculation of well-behaved Green functions. Within this formalism, the pinch technique appears as one of arbitrarily many equivalent possibilities.

Two-loop O( αsGμmt2) corrections to the partial decay width of the Z 0 into [formula omitted] final states in the large top-mass limit

The QCD correction to the one-loop electroweak radiative correction of the partial Z-decay width into b-quarks is calculated analytically in the limit of large top mass. The calculation is performed in the 't Hooft gauge with an arbitrary gauge parameter and QCD gauge-invariance is explicitly verified on-shell. Gluon bremsstrahlung is taken into account by integrating over the whole gluon phase space. All calculations, including the bremsstrahlung, are performed in the dimensional regularization scheme. We find a screening of the leading one-loop top mass effects by m t 2→m t 2 [1− 1 3 (π 2−3)α s π ] which is of the same magnitude as the one known for the ϱ-parameter.

Closed-form bound-state effective potential and exact solutions for dynamical symmetry breaking in a 4D gauge theory

We have found a closed-form expression for the bound-state effective potential or a large class of models of dynamical symmetry breaking. Exact solutions to a Schwinger-Dyson equation and the corresponding Bethe-Salpeter equations are found. This enables one to cómpute the effective potential in a non-trivial four-dimensional gauge model of chiral breaking for an arbitrary coupling constant and gauge parameter.

Gauge theory and effective lagrangians

We extend our previous methods to show how to find the effective lagrangian for non-abelian gauge theories quantized in the covariant gauge for arbitrary gauge parameter α. We explicitly calculate the effective lagrangian to the two-loop level. The inductive algorithm used to carry out this calculation is applicable to any quantum field theory, evaluated to any finite order of perturbation theory.

Subsidiary conditions and physical S-matrix unitary in covariant canonical formulation of supergravity

A canonical operator formalism of supergravity in covariant gauges is presented in the framework of indefinite-metric quantum field theory. In order to specify the invariant physical subspace by a simple subsidiary condition Q B|phys〉=0 with the help of the BRS charge Q B, it is found necessary to adopt an unconventional form of spinor-FP-ghost Lagrangian i c ̄ ∗∂/ D ̷ c slightly different from the usual one c ̄ ∗ D ̷ c . By clarifying the metric structure of the total Fock space spanned by the asymptotic fields, the physical S-matrix unitarity for arbitrary gauge parameters is proved. This unitarity proof is also made simpler by the present choice of FP-ghost Lagrangian. The relationship between the present FP-ghost Lagrangian and the conventional one is also made clear.