Quantum mechanics of the vacuum state in two-dimensional QCD with adjoint fermions

Journal Article · Thu Jun 15 04:00:00 EDT 1995 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.51.7060· OSTI ID:63645

Lenz, F ^[1]; Shifman, M ^[2]; Thies, M ^[1]

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1. Institute for Theoretical Physics, University of Erlangen-Nuernberg, Staudtstrasse 7, 91058 Erlangen (Germany)
2. Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455 (United States)

A study of two-dimensional QCD on a spatial circle with Majorana fermions in the adjoint representation of the gauge groups SU(2) and SU(3) is performed. The main emphasis is put on the symmetry properties related to the homotopically nontrivial gauge transformations and the discrete axial symmetry of this model. Within a gauge-fixed canonical framework, the delicate interplay of topology on the one hand and Jacobians and boundary conditions arising in the course of resolving Gauss`s law on the other hand is exhibited. As a result, a consistent description of the residual {ital Z}{sub {ital N}} gauge symmetry [for SU({ital N})] and the ``axial anomaly`` emerges. For illustrative purposes, the vacuum of the model is determined analytically in the limit of a small circle. There, the Born-Oppenheimer approximation is justified and reduces the vacuum problem to simple quantum mechanics. The issue of fermion condensates is addressed and residual discrepancies with other approaches are pointed out.

• Research Organization: University of Minnesota
• DOE Contract Number: FG02-94ER40823; FC02-94ER40818
• OSTI ID: 63645
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 12 Vol. 51; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BORN-OPPENHEIMER APPROXIMATION
BOUNDARY CONDITIONS
FERMIONS
GAUGE INVARIANCE
QUANTUM CHROMODYNAMICS
QUANTUM MECHANICS
SU-2 GROUPS
SU-3 GROUPS
TOPOLOGY
TRANSFORMATIONS
TWO-DIMENSIONAL CALCULATIONS
VACUUM STATES