Worldline Formalism and Noncommutative Theories

Abstract: The objective of this Ph.D. thesis is the implementation of the Worldline Formalism in the frame of Noncommutative Quantum Field Theories. The result is a master formula for the 1-loop effective action that is applied to a number of scalar models -- among them the Grosse-Wulkenhaar model. As a byproduct we find an expression for the small propertime expansion of general nonlocal operators' Heat Kernel. As an introduction, basic notions of spectral functions, Quantum Field Theories --path integrals and renormalization by means of spectral functions-- and the Worldline Formalism for commutative theories are given.