The Path Integral for the Loop Representation of Lattice Gauge Theories

Abstract

We show how the Hamiltonian lattice loop representation can be cast straightforwardly in the path integral formalism. The procedure is general for any gauge theory. Here we present in detail the simplest case: pure compact QED. We also analyze the non-Abelian Yang-Mills theory. The lattice loop path integral approach allows to knit together the power of statistical algorithms with the transparency of the gauge invariant loop description. The results produced by numerical simulations with the loop classical action for different lattice models are discused.

8 pages, REVTEX, 1 Encapsulated Postscript figure using psfig

References in corpus (4)

• Discreteness of area and volume in quantum gravity
• The Lagrangian Loop Representation of Lattice U(1) Gauge Theory
• Loop Action for Lattice U(1) Gauge Theory
• Matter Fields in the Lagrangian Loop Representation: Scalar QED

Cited by in corpus (6)

• The basis of the physical Hilbert space of lattice gauge theories
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• On the Path Integral Loop Representation of (2+1) Lattice Non-Abelian Theory
• Bibliography of publications related to Classical and Quantum Gravity in terms of Connection and Loop Variables
• Multisymplectic effective General Boundary Field Theory
• Numerical Computations in the Worldsheet Formulation