Accession Number : AD0702075
Title : ALGEBRAIC AND GEOMETRIC STRUCTURES IN CURRENT ALGEBRA THEORY.
Descriptive Note : Technical rept.,
Corporate Author : INSTITUTE FOR ADVANCED STUDY PRINCETON N J
Personal Author(s) : Hermann,Robert
Report Date : FEB 1970
Pagination or Media Count : 120
Abstract : The paper begins the general mathematical study of 'current algebras' by elementary particle physicists. They are defined abstractly as infinite dimensional real Lie algebras, whose underlying vector space is a module over the ring of test-functions. Preliminary remarks about classification of these objects and general geometric and algebraic methods of their construction are made. As preparation, certain facts about differential operators on arbitrary modules are presented. In addition, remarks about the differential-geometric nature of the 'energy-momentum tensor' and conformal symmetry are made. Finally, a global transformation group is constructed whose Lie algebra is one of the simplest current algebras.
Descriptors : (*ALGEBRAS, *FIELD THEORY), ELEMENTARY PARTICLES, OPERATORS(MATHEMATICS), TRANSFORMATIONS(MATHEMATICS), DIFFERENTIAL GEOMETRY, VECTOR SPACES, TENSOR ANALYSIS, INVARIANCE, CALCULUS OF VARIATIONS, THEOREMS
Subject Categories : Theoretical Mathematics
Nuclear Physics & Elementary Particle Physics
Quantum Theory and Relativity
Distribution Statement : APPROVED FOR PUBLIC RELEASE