Quantum Fluctuations versus Topology - a Study in U(1)_2 Lattice Gauge Theory

Abstract

Using the geometric definition of the topological charge we decompose the path integral of 2-dimensional U(1) lattice gauge theory into topological sectors. In a Monte Carlo simulation we compute the average value of the action as well as the distribution of its values for each sector separately. These numbers are compared with analytic lower bounds of the action which are relevant for classical configurations carrying topological charge. We find that quantum fluctuations entirely dominate the path integral. Our results for the probability distribution of the Monte Carlo generated configurations among the topological sectors can be understood by a semi-phenomenological argument.

11 pages, 3 figures

Cited by in corpus (15)

• The index theorem in QCD with a finite cut-off
• Lattice Study of the Massive Schwinger Model with $\theta$ Term under Lüscher's "Admissibility" Condition
• On the spectrum of the Wilson-Dirac lattice operator in topologically non-trivial background configurations
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Mass spectrum and elastic scattering in the massive SU(2)_f Schwinger model on the lattice
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• Properties of the Fixed Point Lattice Dirac Operator in the Schwinger Model
• Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions
• Sum Rules for the Dirac Spectrum of the Schwinger Model
• QCD in a finite box: Numerical test studies in the three Leutwyler-Smilga regimes
• Proposal for Topologically Unquenched QCD
• Dominance of a single topological sector in gauge theory on non-commutative geometry
• Topologically Unquenched QCD: Prospects from an explorative study in 2-flavour QED(2)
• Dirac zero-modes in compact U(1) gauge theory
• Prospects of `Topologically Unquenched QCD' from a study of the analogous importance sampling method in the massive Schwinger model