Worldline Formalism and Noncommutative Theories

TL;DR

This thesis develops a master formula within the Worldline Formalism for noncommutative quantum field theories, enabling analysis of 1-loop effective actions and heat kernel expansions for scalar models.

Contribution

It introduces a novel application of the Worldline Formalism to noncommutative theories, providing tools for calculating effective actions and heat kernels in this context.

Findings

Derived a master formula for 1-loop effective actions in noncommutative theories

Applied the formalism to scalar models including the Grosse-Wulkenhaar model

Obtained an expression for the small propertime expansion of nonlocal operators' Heat Kernel

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.