A Non-Abelian Fourier Transform for Gauge Theories

Details A Non-Abelian Fourier Transform for Gauge Theories A Non-Abelian Fourier Transform for Gauge Theories

2001-11-30

arxiv.org/abs/hep-th/0111286v1

Phys.Rev. D65 (2002) 125004

Physics

High Energy Physics

High Energy Physics - Theory

12 pages

Scientific paper

10.1103/PhysRevD.65.125004

We consider SU(2) gauge potentials over a space with a compactified dimension. A non-Abelian Fourier transform of the gauge potential in the compactified dimension is defined in such a way that the Fourier coefficients are (almost) gauge invariant. The functional measure and the gauge field strengths are expressed in terms of these Fourier coefficients. The emerging formulation of the non-Abelian gauge theory turns out to be an Abelian gauge theory of a set of fields defined over the initial space with the compactified dimension excluded. The Abelian theory contains an Abelian gauge field, a scalar field, and an infinite tower of vector matter fields, some of which carry Abelian charges. Possible applications of this formalism are discussed briefly.

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