Perturbative Gauge Invariance Research Articles

Gauge Anomaly Associated with the Majorana Fermion in 8k + 1 Dimensions

Using an elementary method, we show that an odd number of Majorana fermions in $8k+1$ dimensions suffer from a gauge anomaly that is analogous to the Witten global gauge anomaly. This anomaly cannot be removed without sacrificing the perturbative gauge invariance. Our construction of higher-dimensional examples ($k geq1$) makes use of the SO(8) instanton on $S^8$.

Proof of perturbative gauge invariance for tree diagrams to all orders

It is proved that classical BRS-invariance of the Lagrangian implies perturbative gauge invariance for tree diagrams to all orders. The proof applies in particular to the Einstein Hilbert Largrangian of gravity.

Proof of perturbative gauge invariance for tree diagrams to all orders

AbstractIt is proved that classical BRS‐invariance of the Lagrangian implies perturbative gauge invariance for tree diagrams to all orders. The proof applies in particular to the Einstein Hilbert Lagrangian of gravity.

Scalar Matter Coupled to Quantum Gravity in the Causal Approach: One-Loop Calculations and Perturbative Gauge Invariance

Quantum gravity coupled to scalar massive matter fields is investigated in the framework of causal perturbation theory using the Epstein–Glaser regularization/renormalization scheme. Detailed one-loop calculations include the matter loop graviton self-energy and the matter self-energy. The condition of perturbative operator gauge invariance to second order implies the usual Slavnov–Ward identities for the graviton two-point connected Green function in the loop graph sector and generates the correct quartic graviton-matter interaction in the tree graph sector. The mass zero case is also discussed.

One-loop calculations in quantumgravity: graviton self-energy, perturbative gauge invariance and Slavnov-Wardidentities

In this paper we calculate the one-loop graviton self-energy within theframework of causal perturbation theory. Because of thisregularization/renormalization scheme, the result is ultraviolet finite,without introducing counterterms, and cut-off-free. In addition, it satisfiesthe gravitational Slavnov-Ward identities for the two-point connectedGreen function. The latter are also investigated from the point of viewof a perturbative formulation of operator gauge invariance. Then, thecondition of perturbative gauge invariance to second order for loop graphsis proved. Corrections to the Newtonian potential coming from thegraviton self-energy are also derived.

General massive gauge theory

The concept of perturbative gauge invariance formulated exclusively by means of asymptotic fields is used to construct massive gauge theories. We consider the interactions of $r$ massive and $s$ massless gauge fields together with $(r+s)$ fermionic ghost and anti-ghost fields. First order gauge invariance requires the introduction of unphysical scalars (Goldstone bosons) and fixes their trilinear couplings. At second order additional physical scalars (Higgs fields) are necessary, their coupling is further restricted at third order. In case of one physical scalar all couplings are determined by gauge invariance, including the Higgs potential. For three massive and one massless gauge field the $SU(2)\times U(1)$ electroweak theory comes out as the unique solution.

Perturbative gauge invariance: the electroweak theory

The concept of perturbative gauge invariance formulated exclusively by means of asymptotic fields is generalized to massive gauge fields. Applying it to the electroweak theory leads to a complete fixing of couplings of scalar and ghost fields and of the coupling to leptons, in agreement with the standard theory. The W/Z mass ratio is also determined, as well as the chiral character of the fermions. We start directly with massive gauge fields and leptons and, nevertheless, obtain a theory which satisfies perturbative gauge invariance.

Perturbative gauge invariance: the electroweak theory

AbstractThe concept of perturbative gauge invariance formulated exclusively by means of asymptotic fields is generalized to massive gauge fields. Applying it to the electroweak theory leads to a complete fixing of couplings of scalar and ghost fields and of the coupling to leptons, in agreement with the standard theory. The W/Z mass ratio is also determined, as well as the chiral character of the fermions. We start directly with massive gauge fields and leptons and, nevertheless, obtain a theory which satisfies perturbative gauge invariance.

Gauge independence of theS-matrix in the causal approach

The gauge dependence of the time-ordered products for Yang-Mills theories is analysed in perturbation theory by means of the causal method of Epstein and Glaser together with perturbative gauge invariance. This approach allows a simple inductive proof of the gauge independence of the physical S-matrix.

On gauge invariance and spontaneous symmetry breaking

We show how the widely used concept of spontaneous symmetry breaking can be explained in causal perturbation theory by introducing a perturbative version of quantum gauge invariance. Perturbative gauge invariance, formulated exclusively by means of asymptotic fields, is discussed for the simple example of Abelian U(1) gauge theory (Abelian Higgs model). Our findings are relevant for the electroweak theory, as pointed out elsewhere.

Gauge invariance in finite QED

Gauge invariance is discussed in the causal approach to QED. It is proven that the iterative construction of theS-matrix by the method of Epstein and Glaser can be carried out in such a way that perturbative gauge invariance holds true. The proof rests on a careful analysis of the process of distribution splitting. In case of nontrivial distribution splitting gauge invariance implies the Ward-Takahashi identities.