Loop Variables for compact two-dimensional quantum electrodynamics

Details Loop Variables for compact two-dimensional quantum electrodynamics Loop Variables for compact two-dimensional quantum electrodynamics

1997-12-09

arxiv.org/abs/hep-th/9712096v1

Phys.Rev. D57 (1998) 3711-3724

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, 1 figure, to be published in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.57.3711

Variables parametrized by closed and open curves are defined to reformulate compact U(1) Quantum Electrodynamics in the circle with a massless fermion field. It is found that the gauge invariant nature of these variables accommodates into a regularization scheme for the Hamiltonian and current operators that is specially well suited for the study of the compact case. The zero mode energy spectrum, the value of the axial anomaly and the anomalous commutators this model presents are hence determined in a manifestly gauge invariant manner. Contrary to the non compact case, the zero mode spectrum is not equally spaced and consequently the theory does not lead to the spectrum of a free scalar boson. All the states are invariant under large gauge transformations. In particular, that is the case for the vacuum, and consequently the $\theta$-dependence does not appear.

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