Aspects of QED and non-Abelian gauge theories in S/sup 1/not =/sup 3/ and S/sup 1/not =/sup 4/ spacetimes

Journal Article · Sun May 15 00:00:00 EDT 1988 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.37.2853· OSTI ID:5052843

Higuchi, A; Parker, L

We study various aspects of Abelian and non-Abelian gauge field theories in flat spacetime with the topology of S/sup 1/ x R/sup n/ (n = 3,4). We first discuss the effective potential for the electromagnetic field in S/sup 1/ x R/sup 3/ spacetime, with the objective of finding the dependence of coupling constants on the size L of the compactified dimension. It is first necessary to determine the stable vacuum. In particular, a charged scalar field satisfies an effective periodic boundary condition, while a charged spinor field satisfies an effective antiperiodic boundary condition at the stable vacuum. Then we study the effective coupling constants which depend on the size L of the compactified dimension at one-loop level for QED in S/sup 1/ x R/sup 3/ spacetime. In the presence of a charged scalar field, the one-loop correction of one of the effective coupling constants for the lowest Fourier component of the electromagnetic field behaves for small L like 1L, rather than lnL. This is because the lowest Fourier component of the scalar field is constant in the S/sup 1/ direction. The effective coupling constants for higher Fourier components have logarithmic L dependence, but due to collinear singularities (i.e., singularities in self-energy occurring in the limit of zero mass when the virtual particles are on shell and have parallel momenta) the coefficient of the lnL term differs from component to component. We also point out some ambiguities in defining the effective coupling constants. Finally we discuss the effective potential of non-Abelian gauge theories with a charged spinor field in S/sup 1/ x R/sup 4/ spacetime.

• Research Organization: Department of Physics, University of Wisconsin: Milwaukee, Milwaukee, Wisconsin 53201
• OSTI ID: 5052843
• Journal Information: Phys. Rev. D; (United States), Vol. 37:10
• Country of Publication: United States
• Language: English

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