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