GEOMETRIC REGULARIZATION AND GAUGE INVARIANCE IN CHERN–SIMONS THEORIES

• Published in: International journal of modern physics. A, Particles and fields, gravitation, cosmology Vol. 7; no. 2; pp. 235 - 256
• Main Authors: ASOREY, MANUEL, FALCETO, FERNANDO
• Format: Journal Article
• Language: English
• Published: United States World Scientific Publishing Company 20.01.1992
• Subjects: 661100 > Classical & Quantum Mechanics > (1992-); CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COUPLING CONSTANTS; FIELD THEORIES; GAUGE INVARIANCE; GEOMETRY; INVARIANCE PRINCIPLES; MATHEMATICS 662110 > General Theory of Particles & Fields > Theory of Fields & Strings > (1992-); NONLINEAR PROBLEMS; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; RENORMALIZATION; SPACE-TIME; THREE-DIMENSIONAL CALCULATIONS; TOPOLOGY; WILSON LOOP; YANG-MILLS THEORY
• ISSN: 0217-751X; 1793-656X
• DOI: 10.1142/S0217751X92000156

Some perturbative aspects of Chern–Simons theories are analyzed in a geometric-regularization framework. In particular, we show that the independence from the gauge condition of the regularized theory, which insures its global meaning, does impose a new constraint on the parameters of the regularization. The condition turns out to be the one that arises in pure or topologically massive Yang–Mills theories in three-dimensional space–times. One-loop calculations show the existence of nonvanishing finite renormalizations of gauge fields and coupling constant which preserve the topological meaning of Chern–Simons theory. The existence of a (finite) gauge-field renormalization at one-loop level is compensated by the renormalization of gauge transformations in such a way that the one-loop effective action remains gauge-invariant with respect to renormalized gauge transformations. The independence of both renormalizations from the space–time volume indicates the topological nature of the theory.