Table of Contents
Advances in Optical Technologies
Volume 2010, Article ID 798983, 7 pages
Research Article

Asymptotic Principal Values and Regularization Methods for Correlation Functions with Reflective Boundary Conditions

Department of Physics, Graduate School of Engineering, University of Fukui, Fukui 910-8507, Japan

Received 26 November 2009; Accepted 12 March 2010

Academic Editor: Igor I. Mokhun

Copyright © 2010 Masafumi Seriu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce a concept of asymptotic principal values which enables us to handle rigorously singular integrals of higher-order poles encountered in the computation of various quantities based on correlation functions of a vacuum. Several theorems on asymptotic principal values are proved, and they are expected to become bases for investigating and developing some classes of regularization methods for singular integrals. We make use of these theorems for analyzing mutual relations between some regularization methods, including a method naturally derived from asymptotic principal values. It turns out that the concept of asymptotic principal values and the theorems for them are quite useful in this type of analysis, providing a suitable language to describe what is discarded and what is retained in each regularization method.