Probabilistic and differential geometric methods for relativistic and Euclidean Dirac and radiation fields

Abstract

The main objective of the thesis is to study relativistic and Euclidean Fermionic quantum fields from a geometrical and probabilistic point of view as opposed to the standard treatment which is more algebraic in nature.<br /> The main motivation lays in the practical need of being able to apply to Fermionic systems a number of results from probability theory, stochastic analysis, calculus of variations, and infinite dimensional analysis which are readily available in the case of Bosonic quantum fields.<br /> A more general context for this work is the development of alternative models for Fermionic quantum fields.