The mathematical and philosophical foundations of quantum field theory

• Main Author: Saunders, Simon Wolfe
• Published: King's College London (University of London) 1988
• Subjects: 530.1; Theoretical physics
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320350

The thesis is primarily concerned with these objectives: to say what is a quantum field theory, and to explain why and how relativistic quantum field theory differs from non-relativistic quantum field theory, even in the free or weakly interacting (quasi-free) case. Following the ideas of Irving Segal, I shall establish that in this case there is an essential identity in structure of the non-relativistic and relativistic field theories. Novel but straightforward applications of this theory are made to the complex scalar field,and in relation to t.he Dirac hole theory. Although the structure of the relativistic and non-relativistic quasi-free theories is essentially identical, the concept of localization finds different expressions. This plays a fundamental role when interactions are introduced, and leads to two quite distinct notions of causality. I shall confine the detailed study to the massive scalar and spin 1/2 linear field theories, for the most part in the quasi-free case. Not even the latter are trivial, for they descri,be the observed phenomenology and are therefore of central empistemological importance to relativistic quantum theory. I al so advance a general interpretat i ve framework for the philosophical analysis of quantum theory. This is essent ially a real ist interpretation founded on abstract • C -algebras, and it is applied to the measurement problem. The physical and mathematical theories that I draw upon are developed in a historical context. The mathematical theory is presented in a largely heuristic way.