Study of the phase structure of Abelian field theories through non- lattice, non-perturbative calculations (Q1081141)

A recently proposed approach to gauge field theories, by which one formulates them from non-locally and subsequently approaches locality arbitrarily close, is applied to U(1) gauge theories. We test the possibility that the aforementioned methodology might introduce a measure in the functional integral which supports non-perturbative calculations in the continuum. In particular, we are able to carry relevant calculations pertaining to the expectation value of Wilson's loop operator in \(3+1\), \(2+1\) and \(1+1\) dimensions. The results are similar to one obtained through the lattice regularization of U(1) gauge theory, with the important difference that in our case they refer to continuum U(1) gauge theory, as a function of the bare coupling constant. We further solidify the validity of our approach by conducting a calculation referring to the 2-dimensional scalar Heisenberg model, remaining always in the continuum.