# Accession Number:

## AD0711404

# Title:

## THEORY AND APPLICATIONS OF PADE APPROXIMANTS AND QUANTUM FIELD THEORY.

# Descriptive Note:

## Final scientific rept. Oct 68-Jun 70,

# Corporate Author:

## KENT UNIV CANTERBURY (ENGLAND) MATHEMATICAL INST

# Personal Author(s):

# Report Date:

## 1970-07-29

# Pagination or Media Count:

## 13.0

# Abstract:

Preliminary investigations of the application of the Pade technique to sequences of approximants to single-variable integrals show that existing integration methods can be improved upon, particularly when the integrands are singular or are infinitely oscillating. Series of derivatives of delta-functions have been investigated a term-by-term as a generalised function and b by forming Pade Approximants of the Fourier transformed series. When the latter series is a series of Stieltjes, convergence of the approximants in interpretation b is established, to the generalised function defined by interpretation a. Study has begun on solving linear integral equations of the form f g lambda Kf by forming the Pade approximant of the Neumann series. The method appears to work, but is dependent upon the accuracy of performing multiple integrals, which is to be studied under a above. Simple algorithms have been established which enable easy extraction of magnetic moment contributions from vertex parts in field theory. Author

# Descriptors:

# Subject Categories:

- Numerical Mathematics
- Nuclear Physics and Elementary Particle Physics
- Quantum Theory and Relativity