Accession Number : AD0722477

Title :   Quantum Field Theory, Differential Operators and Scattering Theory.

Descriptive Note : Final rept. 1 Mar 68-28 Feb 71,

Corporate Author : STANFORD UNIV CALIF DEPT OF MATHEMATICS

Personal Author(s) : Cohen,Paul J.

Report Date : FEB 1971

Pagination or Media Count : 5

Abstract : The research of this contract has covered several areas, including differential equations, harmonic analysis, functional analysis, logic, and quantum field theory. Some work has been done on the theoretical foundations of field theory while other work has been done on the classical problems in scattering theory arising from the physical situations. In harmonic analysis, questions about function spaces of analytic functions in more than one variable and classical problems in potential theory have been investigated. Tauberian theorems in their relation to number theory, and the general scope of the analytic methods of harmonic analysis in the theory of distribution of prime numbers have been considered. In Logic problems in the existence of models with automorphisms as well as general decision problems were investigated. Some recent results concern the application of automata in deciding various second order theories. Also work was done which offers hope of giving constructive estimates for problems in Diophantine Equations for which only non-constructive methods now exist. (Author)

Descriptors :   (*FUNCTIONAL ANALYSIS, REPORTS), (*FIELD THEORY, QUANTUM THEORY), SET THEORY, NUMBER THEORY, POTENTIAL THEORY, DIFFERENTIAL EQUATIONS, HARMONIC ANALYSIS, MATRICES(MATHEMATICS), ANALYTIC FUNCTIONS, POTENTIAL SCATTERING, GROUPS(MATHEMATICS)

Subject Categories : Theoretical Mathematics
      Quantum Theory and Relativity

Distribution Statement : APPROVED FOR PUBLIC RELEASE