Quantum Fluctuations versus Topology - a Study in U(1) 2 Lattice Gauge Theory

Using the geometric deenition 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 conngura-tions carrying topological charge. We nd that quantum uctuations entirely dominate the path integral. Our results for the probability distribution of the Monte Carlo generated conngurations among the topological sectors can be understood by a semi-phenomenological argument .