The Study of Hyperfunction Quantum Field Theory
Project/Area Number  10640174 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Basic analysis

Research Institution  The University of Tokushima 
Principal Investigator 
NAGAMACHI Shigeaki The University of Tokushima, Faculty of Engineering, Professor, 工学部, 教授 (00030784)

CoInvestigator(Kenkyūbuntansha) 
OKAMOTO Kuniya The University of Tokushima, Faculty of Engineering, Lecturer, 工学部, 講師 (90263871)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥2,000,000 (Direct Cost : ¥2,000,000)
Fiscal Year 1999 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1998 : ¥1,100,000 (Direct Cost : ¥1,100,000)

Keywords  hyperfunction / quantum field / operator algebra / 場の量子論 / 超関数 
Research Abstract 
The relativity and quantum mechanics, which are big discoveries in physics in the 20th century, are combined into the quantum field theory, which is relativistic quantum mechanics. The quantum field theory is characterized by its Wightman functions. The Wightman functions are generalized functions and usually we consider the so called the standard quantum field theory, where the Wightman functions are Schwartz's tempered distributions. The hyperfunction is considered to be the most general one among generalized functions that has the local properties. Therefore the quantum fields which correspond to hyperfunctions (more precisely, the quantum field whose Wightman functions are Fourier hyperfunctions) are considered to be the most general and studied since 1976 by the author. Since the testfunction space of Fourier hyperfunctions consists of analytic functions, it does not contain functions of compact supports. This fact makes the study of hyperfunction quantum field theory (HFQFT) difficult. This time, we have the following results: (1) Since there are no functions with compact supports in the testfunction space of Fourier hyperfunctions, we cannot define the field operator restricted in the bounded region in the framework of HFQFT. Nevertheless we could prove that we can define the operators and operator algebras which correspond to the observables in the bounded region (1998). (2) We proved the existence of the model of HFQFT which has the nontrivial operator algebras which correspond to the set of observables in the bounded region.

Report
(4results)
Research Output
(7results)