Gauge invariant action for (2+1)-dimensional topologically massive Yang--Mills theory

Journal Article · Sun Jun 01 00:00:00 EDT 1986 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(86)90160-0· OSTI ID:5569825

Gonzales, D; Redlich, A N

Under homotopically non-trivial gauge transformations, U-italic/sub n-italic/, with winding number n-italic, the action, I-italic, for topologically massive Yang--Mills theory changes by 2..pi..n-italic:I-italic..-->..I-italic+2..pi..n-italic. Equivalently, Gauss' law requires the physical states Psi/sub phs/(A-italic) to change by a phase under time-independent gauge transformations: A-italic/sup U-italic/ = U-italic/sup dagger/A-italicU-italic+U-italic/sup dagger/partialU-italic, Psi/sub phs/(A-italic/sup U-italic/) = exp(-i-italic..cap alpha..(A-italic,U-italic)) Psi/sub phs/(A-italic). By a unitary transformation, Psi'(A-italic) = e-italic/sup i-italic//sup w-italic//sup (//sup A-italic//sup )/Psi(A-italic), we remove this phase (the Gauss law condition becomes the usual Psi'/sub phs/(A-italic/sup U-italic/) = Psi'/sub phs/(A-italic)) and find a new action, I-italic', which is manifestly gauge invariant, but is spatially non-local and not manifestly Lorentz invariant. W-italic(A-italic) is proportional to the one-loop chiral fermion effective action, -i-italic ln det(partial+A-italic) in two dimensions. In the primed system, analysis of the wave functional Psi'/sub phs/(A-italic) near points in gauge function space where the two-dimensional chiral determinant, det(partial+A-italic), vanishes leads to quantization of the mass parameter ..mu... We use our results to comment upon the connection between the (2n-italic+1)-dimensional non-perturbative anomaly and anomalies in one higher and one lower dimension.

• Research Organization: Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
• OSTI ID: 5569825
• Journal Information: Ann. Phys. (N.Y.); (United States), Vol. 169:1
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
QUANTUM MECHANICS
GAUGE INVARIANCE
YANG-MILLS THEORY
FUNCTIONALS
LAGRANGIAN FUNCTION
SCHROEDINGER EQUATION
UNITARY SYMMETRY
WAVE FUNCTIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
INVARIANCE PRINCIPLES
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
SYMMETRY
WAVE EQUATIONS
645400* - High Energy Physics- Field Theory
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics