# Accession Number:

## AD0420463

# Title:

## AN ANALYTIC REPRESENTATION OF THE INVARIANT DISTRIBUTIONS OF QUANTUM FIELD THEORY,

# Descriptive Note:

# Corporate Author:

## STANFORD UNIV CALIF APPLIED MATHEMATICS AND STATISTICS LABS

# Personal Author(s):

# Report Date:

## 1963-07-26

# Pagination or Media Count:

## 177.0

# Abstract:

It is generally recognized that the invariant functions of quantum field theory are not functions in the strict sense, but rather distributions. One may interpret such distributions in either of two mathematically equivalent but conceptually different ways. They may be considered as generalized limits of sequences of functions, usually called generalized functions. Or they may be considered as continuous linear functionals on suitably chosen space of test functions. There are treatments of the distributions that arise as commutators and propagators in quantum field theory and the term invariant distribution is used in the sense of both the above interpretations of them. Author

# Descriptors:

- *FIELD THEORY
- *FUNCTIONAL ANALYSIS
- *COMPLEX VARIABLES
- MATHEMATICAL ANALYSIS
- CONFORMAL MAPPING
- FUNCTIONS(MATHEMATICS)
- SEQUENCES(MATHEMATICS)
- INTEGRALS
- VECTOR ANALYSIS
- NUMERICAL INTEGRATION
- MATRICES(MATHEMATICS)
- OPERATORS(MATHEMATICS)
- SPECIAL FUNCTIONS(MATHEMATICS)
- TRANSFORMATIONS(MATHEMATICS)
- INEQUALITIES
- INTEGRAL TRANSFORMS