The Freedman-Townsend model in two and three dimensions

Journal Article · Fri Apr 10 04:00:00 EDT 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X92000880· OSTI ID:5138330

Mckeon, D G.C. ^[1]

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1. Dept. of Applied Mathematics, Univ. of Western Ontario, London N6A 5B9 (CA)

In this paper using a mechanism similar to that employed by Freedman and Townsend in four dimensions, the authors discuss a variety of two- and three-dimensional gauge theories. The simplest of these models is equivalent to the nonlinear sigma model; another corresponds to a massive vector theory. In three dimensions, there exists a gauge invariance associated with the auxiliary vector {pi}{sup a}{sub {mu}}; when the authors quantize, this is accommodated using both the Batalin-Vilkovisky configuration space formalism and the Batalin-Fradkin-vilkovisky configuration space formalism. Explicit one-loop calculations in the simplest two-dimensional model are carried out. The regularization used is a variant of operator regularization, allowing one to remain in two dimensions, hence circumventing problems associated with definition of the antisymmetric tensor {xi}{sub {mu} {nu}}. This model is renormalizable, with renormalization mixing the scalar field {pi}{sup a} and the transverse component of the vector field V{sup a}{sub {mu}}.

• OSTI ID: 5138330
• Journal Information: International Journal of Modern Physics A; (United States), Journal Name: International Journal of Modern Physics A; (United States) Vol. 7:9; ISSN IMPAE; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
662120 -- General Theory of Particles & Fields-- Symmetry
Conservation Laws
Currents & Their Properties-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSON-EXCHANGE MODELS
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MIXING RATIO
NONLINEAR PROBLEMS
PARTICLE MODELS
PERIPHERAL MODELS
QUANTIZATION
RENORMALIZATION
SCALAR FIELDS
SIGMA MODEL
SPACE
SYMMETRY
TENSORS
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
VECTOR FIELDS