Um estudo dos efeitos das compactações dimensionais nas teorias de campos

Abstract

The motivation of this work is to refine the understanding about the field theories defined in compactified Euclidean spaces through boundary conditions imposed to some of its dimensions. This construction can be interpreted as a generalization of the finite temperature field theory, proposed mainly by Matsubara, to include spatial limitations. Therefore, from modified Feynman rules, Green functions in Fourier space assume a mixed representation of series and integrals. In this thesis, a study was made of the convergence of these series and their relationship to well known functions such as Riemann’s zeta (and its generalizations) and the modified Bessel functions of the second kind. A criticality analysis of this theory (at one loop) is also made and how a theory with compact dimensions differs from its non-compact counterpart with respect to the superficial degree of convergence, analyzed via Weinberg’s theorem.At last, a prescription is presented for the contribution of a generic Feynman diagram with compactified dimensions for bosonic and fermionic theories.