Nonperturbative quantization of the electroweak model’s electrodynamic sector

M. P. Fry
Phys. Rev. D 91, 085026 – Published 21 April 2015

Abstract

Consider the Euclidean functional integral representation of any physical process in the electroweak model. Integrating out the fermion degrees of freedom introduces 24 fermion determinants. These multiply the Gaussian functional measures of the Maxwell, Z, W, and Higgs fields to give an effective functional measure. Suppose the functional integral over the Maxwell field is attempted first. This paper is concerned with the large amplitude behavior of the Maxwell effective measure. It is assumed that the large amplitude variation of this measure is insensitive to the presence of the Z, W, and H fields; they are assumed to be a subdominant perturbation of the large amplitude Maxwell sector. Accordingly, we need only examine the large amplitude variation of a single QED fermion determinant. To facilitate this the Schwinger proper time representation of this determinant is decomposed into a sum of three terms. The advantage of this is that the separate terms can be nonperturbatively estimated for a measurable class of large amplitude random fields in four dimensions. It is found that the QED fermion determinant grows faster than exp[ce2d4xFμν2], c>0, in the absence of zero mode supporting random background potentials. This raises doubt on whether the QED fermion determinant is integrable with any Gaussian measure whose support does not include zero mode supporting potentials. Including zero mode supporting background potentials can result in a decaying exponential growth of the fermion determinant. This is prima facie evidence that Maxwellian zero modes are necessary for the nonperturbative quantization of QED and, by implication, for the nonperturbative quantization of the electroweak model.

  • Received 19 February 2015

DOI:https://doi.org/10.1103/PhysRevD.91.085026

© 2015 American Physical Society

Authors & Affiliations

M. P. Fry

  • University of Dublin, Trinity College, Dublin 2, Ireland

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Issue

Vol. 91, Iss. 8 — 15 April 2015

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