Renormalization and pseudodifferential operators

被引：0

作者：

Uchikoshi, Keisuke ^{[1
]}

机构：

[1] Natl Def Acad, Dept Math, Yokosuka, Kanagawa 2398686, Japan

来源：

JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS | 2025年 / 16卷 / 03期

关键词：

Pseudodifferential operators; Distribution product; Quantum field theory; REGULARIZATION;

D O I：

10.1007/s11868-025-00707-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the product of the kernel functions of two pseudodifferential operators. In general, this product is not well-defined in the usual distribution sense. Using the regularization method in quantum field theory, we show that we can define this product for a class of pseudodifferential operators. Furthermore, we show that such a product again defines a pseudodifferential operator.

引用

页数：28

共 10 条

[1]

[Anonymous], 1987, WATER RES

[2]

Collins J.C., 1986, Renormalization: An Introduction to Renormalization, the Renormalization Group, and the Operator-Product Expansion, DOI DOI 10.1017/CBO9780511622656

[3]

Colombeau J. F., 1984, NEW GEN FUNCTIONS MU

[4]

GELFAND IM, 1964, GEN FUNCTIONS, V1

[5]

Hormander L., 1990, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, V2

[6]

Lesch M., 2010, Clay Math. Proc, V12, P37

[7] ON THE INVARIANT REGULARIZATION IN RELATIVISTIC QUANTUM THEORY [J].

PAULI, W ;

VILLARS, F .

REVIEWS OF MODERN PHYSICS, 1949, 21 (03) :434-444

[8]

Peskin M., 1989, An Introduction to Quantum Field Theory

[9] ANALYTIC FUNCTIONALS IN QUANTUM FIELD THEORY AND REGULARIZATION OF ULTRAVIOLET DIVERGENCES [J].

THIESS, FB .

JOURNAL OF MATHEMATICAL PHYSICS, 1968, 9 (02) :305-&

[10] REGULARIZATION AND RENORMALIZATION OF GAUGE FIELDS [J].

THOOFT, G ;

VELTMAN, M .

NUCLEAR PHYSICS B, 1972, B-44 (01) :189-+

← 1 →