Testing gauge-invariant perturbation theory

TL;DR

This paper reviews gauge-invariant perturbation theory, demonstrating its application, comparing it with conventional perturbation theory, and testing its predictions against lattice gauge theory results in various scenarios.

Contribution

It shows how gauge-invariant perturbation theory can be applied, compares it with conventional methods, and provides empirical tests using lattice gauge theory.

Findings

In some cases, gauge-invariant and conventional perturbation theories agree with lattice results.

In other cases, gauge-invariant theory aligns with lattice results while conventional does not.

Both approaches fail in scenarios with strong quantum fluctuations.

Abstract

Gauge-invariant perturbation theory for theories with a Brout-Englert-Higgs effect, as developed by Fr\"ohlich, Morchio and Strocchi, starts out from physical, exactly gauge-invariant quantities as initial and final states. These are composite operators, and can thus be considered as bound states. In case of the standard model, this reduces almost entirely to conventional perturbation theory. This explains the success of conventional perturbation theory for the standard model. However, this is due to the special structure of the standard model, and it is not guaranteed to be the case for other theories. Here, we review gauge-invariant perturbation theory. Especially, we show how it can be applied and that it is little more complicated than conventional perturbation theory, and that it is often possible to utilize existing results of conventional perturbation theory. Finally, we present tests of the predictions of gauge-invariant perturbation theory, using lattice gauge theory, in three different settings. In one case, the results coincide with conventional perturbation theory and with the lattice results. In a second case, it appears that the results of gauge-invariant perturbation theory agree with the lattice, but differ from conventional perturbation theory. In the third case both approaches fail due to quantum fluctuations.