AN ANALYTIC REPRESENTATION OF THE INVARIANT DISTRIBUTIONS OF QUANTUM FIELD THEORY

Thesis/Dissertation · Tue Jan 01 04:00:00 EST 1963

OSTI ID:4010630

Thiess, F B

Invariant distribution'' means any of the commutators and propagators associated with a quantized particle field. It is shown that all the invariant distributions of a given nonlnteracting field are boundary values of one and the same matrix of analytic functions, called the particle kernel'' of the field. The invariant distributions are represented as integral operators on a space of annlytic test functions, where the defining integrations are over 4dimensional hypersurfaces in the 8-dimensional space of 4 complex variables and employ the particle kernels'' as integration kernels. The theory of free particles is examined in the light of these analytic representations'' for the invariant distributions and is shown to possess a structural simplicity and some irteresting symmetry properties. The analytic theory developed for free fields is used to investigate the perturbation treatment of particle interactions. A formalism is given for expressing scattering matrix elemerts in terms of the analytic represertations mentioned above. A study is made of scattering processes, which shows that the analytic formalism developed in this paper is equivalent to the standard formalism of field theory whenever operations within the standard formalism are well defined. When the operations in the standard formalism are not well defined because formal products of invariant distributions occur, these invariant distributions may be multiplied in a very natural way within the analytic formalism. Using an analytically'' defined multiplication for invariant distributions, the singularities that cause the ultraviolet divergences of field theory can be isolated and examined. In the analytic formalism, no delta -functions appear, and consequently the matrix elements of field theory may be evaluated using only operators that are defined within the context of complex analysis. (Dissertation Abstr., 24: No. 8, Feb. 1964)

• Research Organization: Originating Research Org. not identified
• NSA Number: NSA-18-021068
• OSTI ID: 4010630
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

CONFIGURATION
DIFFERENTIAL EQUATIONS
DISTRIBUTION
ELEMENTARY PARTICLES
FIELD THEORY
INTEGRALS
INTERACTIONS
INVARIANCE PRINCIPLE
MATHEMATICS
MATRICES
PERTURBATION THEORY
PHYSICS
QUANTUM MECHANICS
SCATTERING
SINGULARITY
SYMMETRY