Rigorous treatement of θ-states
Tiago de Jesus · cIRcle (University of British Columbia) · 2009
In the last twenty years there has been growing interest in topological effects in Quantum Field Theories (Q.F.T.'s). In particular, the existence of θ-vacuums in Yang-Mills theories has attracted a lot of attention. One problem with these topological effects in Q.F.T.'s is that they are derived using the assumption that field configurations are represented by smooth functions. It is well known that the fields found in (rigorous) Q.F.T.'s are typically distributional and thus the usual topological arguments are not valid. A natural question to ask is: Do θ-vacuums really exist in the rigorous theory of Q.C.D.? Here we construct the rigorous quantum theory of the electromagnetic field on a 3-torus and prove that 6-vacuums exist in this Q.F.T., still exist. Hence, we show the rigorous existence of topological effects in this Q.F.T. and thus provide strong evidence for the existence of θ-vacuums in Q.C.D.