Canonical transformations to action and angle variables and their representation in quantum mechanics. IV. Periodic potentials: J. Flores, G. López, G. Monsivais, and M. Moshinsky. Instituto de Física, UNAM, Apdo. Postal 20-364, 01000 México, D.F., México

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 139 KB
• Volume: 171
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(86)90012-6

✦ Synopsis

A recently proposed approach to gauge held theories. by which one formulates them nonlocally and subsequently approaches locality arbitrarily close, is applied to cI( 1) gauge theories. We test the possibility that the aformentioned 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 + I, 2 + 1, and 1 + 1 dimensions. The results are similar to ones obtained through the lattice regularization of C'( 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.