Lattice Gauge Theories as Problems of Constructive Quantum Field Theory
Project/Area Number  10640161 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Basic analysis

Research Institution  Nagoya Institute of Technology 
Principal Investigator 
YAMAMOTO Kazuhiro Nagoya Institute of Technology, Professor, 工学部, 教授 (30091515)

CoInvestigator(Kenkyūbuntansha) 
IWASHITA Hirokazu Nagoya Institute of Technology, Professor, 工学部, 助教授 (30193741)
NAKAMURA Yosihiro Nagoya Institute of Technology, Assistant Professor, 工学部, 助教授 (50155868)
ADACHI Tosiaki Nagoya Institute of Technology, Assistant Professor, 工学部, 助教授 (60191855)
YOSOMURA Zenichi Nagoya Institute of Technology, Professor, 工学部, 教授 (70047330)
TODA Nobusige Nagoya Institute of Technology, Professor, 工学部, 教授 (30004295)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1999 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1998 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  Renormalization transform / Lattice model / Partition function / Abelian lattice gauge theory / Quantum field theory / 繰り込み変換 / 格子モデル / 分配関数 / 可換格子ゲージ場 / 場の量子論 / 格子ゲージ場理論 / 構成的場の理論 
Research Abstract 
The Aim of this program is to give a mathematically rigid theory for models appeared in quantum field theory. In particular the following two themes are concrete targets ; Ultraviolet stability for Abelian HiggsKibble model in a three dimensional finite lattice, which is a model in quantum electrodynamics, and existence of its continuous limite of the lattice space and the required physical axioms satisfied by the continuous limited space. For two years research we can not get the completely results for the above problems. But we can got the following interesting results. First we can give a rigorous definition of the renormalization transform used in theoretical physics. That is formally defined by making use of Dirac's δ function and one of it's properties, that is, FaddeevPopov procedure is justified by the formal invariance of Haar measure for δfunction. But we defined a renormalization transform as the measure and prove the all required properties. Secondly, we can prove the ultraviolet stability for three dimensional Abelian HiggsKibble model. Now we are preparing this result. In order to verify this uniform estimate we need new WardTakahasi identity appearing in new type graphs.

Report
(4results)
Research Output
(8results)