INEQUIVALENT QUANTIZATIONS OF YANG-MILLS THEORY ON A CYLINDER

Yang-Mills theories on a (1 + 1)-dimensional cylinder are considered. It is shown that canonical quantization can proceed following differen t routes, leading to inequivalent quantizations. The problem of the no n-free action of the gauge group on the configuration space is also di scussed. In particular we re-examine the relationship between ''theta- states'' and the fundamental group of the configuration space. It is s hown that this relationship does or does not hold depending on whether or not the gauge transformations not connected to the identity act fr eely on the space of connections module connected gauge transformation s.