Charges in gauge theories

Abstract

In this article we investigate charged particles in gauge theories. After reviewing the physical and theoretical problems, a method to construct charged particles is presented. Explicit solutions are found in the Abelian theory and a physical interpretation is given. These solutions and our interpretation of these variables as the true degrees of freedom for charged particles, are then tested in the perturbative domain and are demonstrated to yield infra-red finite, on-shell Green's functions at all orders of perturbation theory. The extension to collinear divergences is studied and it is shown that this method applies to the case of massless charged particles. The application of these constructions to the charged sectors of the standard model is reviewed and we conclude with a discussion of the successes achieved so far in this programme and a list of open questions.

Charges from Dressed Matter: Physics and Renormalisation

“…We further note that (13) is essentially identical to the result [6,8] Having thus shown the cancellation of the various IR divergences which occur in the residue of the propagator evaluated in wave-function, on-shell renormalisation, let us move on to a charge being scattered off a source. For the covariant diagram, 4e, we again take the p / + m numerator factors through the interaction vertex γ matrices and only retain those terms which have a pole for each external leg.…”

“…It will be shown that the IR divergences associated with going on-shell are indeed removed already at the level of S-matrix elements at all orders in perturbation theory. (Some similar results for scalar QED have been announced elsewhere [5,6]; here we consider the fermionic theory and give details of our calculations and techniques.) Then the UV structure of these fields will be investigated and it will be shown that the dressed fields have a good UV behaviour.…”

Asymptotic dynamics in quantum field theory

“…The asymptotic dynamics of this theory [20] requires further study, in particular the physical asymptotic fields need to be constructed. Finite temperature field theory is another area where infra-red divergences are important, here, of course, the residual asymptotic dynamics of zero temperature will be acerbated by excitations from the heat bath.…”

“…with the obvious meaning given to the components of J µ defined in (20). We shall work in Feynman gauge and take the plane wave expansions given by…”

“…The cubic term in the interaction Hamiltonian (19), which comes from the J µ 1 term in (20), is made up of two parts, J µ 11 and J µ 12 . These two terms are similar in their structure and both contribute to the problem of infra-red divergences.…”