Perturbative Evaluation of the Effective Action for a Self-Interacting Conformal Field on a Manifold with Boundary

TL;DR

This paper introduces a new technique for higher-loop renormalisation in Euclidean Quantum Field Theory on manifolds with boundaries, analyzing boundary effects on the theory's dynamics.

Contribution

It develops a novel method for higher-loop renormalisation on manifolds with boundaries, enhancing understanding of boundary influences in quantum field theories.

Findings

Effective boundary effects on dynamical behaviour identified

New renormalisation technique applicable to boundary manifolds

Theoretical framework established for boundary quantum field analysis

Abstract

In a series of three projects a new technique which allows for higher-loop renormalisation on a manifold with boundary has been developed and used in order to assess the effects of the boundary on the dynamical behaviour of the theory. Commencing with a conceptual approach to the theoretical underpinnings of the, underlying, spherical formulation of Euclidean Quantum Field Theory this overview presents an outline of the stated technique's conceptual development, mathematical formalism and physical significance.