The Lagrangian Loop Representation of Lattice U(1) Gauge Theory

Abstract

It is showed how the Hamiltonian lattice $loop$ $representation$ can be cast straightforwardly in the Lagrangian formalism. The procedure is general and here we present the simplest case: pure compact QED. This connection has been shaded by the non canonical character of the algebra of the fundamental loop operators. The loops represent tubes of electric flux and can be considered the dual objects to the Nielsen-Olesen strings supported by the Higgs broken phase. The lattice loop classical action corresponding to the Villain form is proportional to the quadratic area of the loop world sheets and thus it is similar to the Nambu string action. This loop action is used in a Monte Carlo simulation and its appealing features are discussed.

13 pp, UAB-FT-341/94

References in corpus (4)

• String Representation of the Abelian Higgs Theory and Aharonov-Bohm Effect on the Lattice
• Fixed boundary conditions and phase transitions in pure gauge compact QED
• The First Order Signal in Pure U(1) Gauge Theory May be Fake
• Loop Action for Lattice U(1) Gauge Theory

Cited by in corpus (9)

• Gauge-ball spectrum of the four-dimensional pure U(1) gauge theory
• On the Path Integral Loop Representation of (2+1) Lattice Non-Abelian Theory
• The Path Integral for the Loop Representation of Lattice Gauge Theories
• Calculation of Wilson loops in 2-dimensional Yang-Mills theories
• Matter Fields in the Lagrangian Loop Representation: Scalar QED
• Phase Transitions in lattice QED
• SU(2) QCD in the Path Representation: General Formalism and Mandelstam Indentities
• Numerical Computations in the Worldsheet Formulation
• Finite Size Analysis of the U(1) Phase Transition using the World-sheet Formulation