LOOP VARIABLES FOR COMPACT 2-DIMENSIONAL QUANTUM ELECTRODYNAMICS

Variables parametrized by closed and open curves are defined to reform ulate compact U(1) quantum electrodynamics in a circle with a massless fermion field. It is found that the gauge-invariant nature of these v ariables accommodates into a regularization scheme for the Hamiltonian and current operators that is especially well suited for the study of the compact case. The zero-mode energy spectrum, the value of the axi al anomaly, and the anomalous commutators this model presents are henc e determined in a manifestly gauge-invariant manner. Contrary to the n oncompact case, the zero-mode spectrum is not equally spaced and conse quently the theory does not lead to the spectrum of a free scalar boso n. All the states are invariant under large gauge transformations. In particular, that is the case for the vacuum, and consequently the thet a dependence does not appear.