QUANTUM NONLOCAL FIELD THEORY: PHYSICS WITHOUT INFINITIES

Abstract

It is argued that nonlocality is an essential ingredient in Relativistic Quantum Field Theory in order to have finite theory without recourse to a renormalisation program. A critical review of the physical constraints on the form the nonlocality can take is presented. The conclusion of this review is that nonlocality must be restricted to interactions with the vacuum sea of virtual particles. A successful formulation of such a theory, QNFT, is applied to scalar electrodynamics and serves to illustrate how gauge invariance and manifest finiteness can be achieved. The importance of the infinite dimensional symmetry groups that occur in QNFT are discussed as an alternative to supersymmetry, the ability to generate masses by breaking the nonlocal symmetry with a noninvariant functional measure is given a critical assessment. To demonstrate some of the many novel applications QNFT may make possible two examples are mooted, the existence of electroweak monopoles and the formulation of a finite perturbative theory of Quantum Gravity.