Field strength formulation of gauge theories

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1982

OSTI ID:5139724

Mendel, E D

In this thesis an alternative to the usual formulation of gauge theories is presented. The usual description in terms of vector field potentials A/sub ..mu../(x) is replaced by a description in terms of field strength tensors F..mu../sub v/(x). This is done in the coordinate gauge, x..mu..A/sub ..mu../(x) = 0, where the vector potentials can be expressed in a simple form in terms of the field strengths. The inversion formula gives a one-to-one correspondence between smooth fields A/sub ..mu../ and F/sub ..mu..v/. Even for singular A/sub ..mu../ configurations, it has been shown that the set of potentials which corresponds to the same F/sub ..mu..v/ (copies) is probably of measure zero in the space of potentials. Furthermore, the field strength tensor in the coordinate gauge has to satisfy the Bianchi identities. As a result the generating functional Z(J) for the quantum field theory may be transformed from an expression in terms of A..mu..(x) to one in terms of fields lambda(sub sigma)x can be introduced to enforce these constraints. The tensor fields F/sub ..mu..v/(x). The Bianchi identities appear as constraints on the allowed class of tensors F/sub ..mu..v(x). A set of Lagrange multiplier fields lambda/sub sigma/(x) can be introduced to enforce these constraints. The tensor fields F/sub ..mu..v/(x) can be integrated out in the functional integral for Z, leaving an expression for Z(J) in terms of the fields lambdasigma(x). This appears to be useful for analyzing the strong coupling limit of the gauge theory. Our results are closely related to, but are much simpler than, Halpern's dual variable formulation of gauge theories in the axial gauge. The Hamiltonian formalism for systems with constraints corresponding to this field strength formulation was also developed for the abelian theory. The results show that the field strength formulation of the gauge theory can be seen as defining a new quantum theory in its own right.

• Research Organization: Wisconsin Univ., Madison (USA)
• OSTI ID: 5139724
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FIELD THEORIES
HAMILTONIANS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
PARTICLE MODELS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
TENSORS
UNIFIED GAUGE MODELS
VECTORS