Field-strength formulation of gauge theories: Transformation of the functional integral

Journal Article · Wed Sep 15 04:00:00 EDT 1982 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.26.1368· OSTI ID:6692818

Durand, L; Mendel, E

We present a formulation of gauge field theories in which the gauge potentials A/sub ..mu../(x) are eliminated in a simple way in terms of the field strengths F/sub munu/(x). Our results are closely related to, but are much simpler than, Halpern's dual variable formulation of gauge theories in the axial gauge. We work in the coordinate gauge x/sup ..mu../A/sub ..mu../(x) = 0, and show both analytically and geometrically that the potential A/sub ..mu../ can be determined uniquely from the field strengths F/sub munu/ for a suitable class of F's, A..-->..A(F). We show, furthermore, that a tensor F/sub munu/(x) is a coordinate-gauge field tensor if and only if it satisfies the restricted set of Bianchi identities epsilon/sup munusigmalambda/x/sub sigma/D/sup rho/(F)*F/sub rholambda/ = 0, D = partial+(A(F),x). These results permit us to transform the functional integral for the vacuum-to-vacuum amplitude Z(J) for the gauge theory to a form in which the potentials are completely eliminated in terms of the field strengths. When the Bianchi constraints are eliminated using a set of Lagrange multiplier fields lambda/sub sigma/(x), the F 's can be integrated out completely to obtain a form of the theory which appears to be useful for strong coupling.

• Research Organization: Physics Department, University of Wisconsin at Madison, Madison, Wisconsin 53706
• OSTI ID: 6692818
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 26:6; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
FIELD THEORIES
FUNCTIONALS
FUNCTIONS
GAUGE INVARIANCE
GREEN FUNCTION
HAMILTONIANS
HILBERT SPACE
INVARIANCE PRINCIPLES
LAGRANGIAN FIELD THEORY
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
PARTICLE MODELS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SPACE
STRONG-COUPLING MODEL