Mathematical problems in quantum field theory and infinite dimensional analysis

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04888
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Hokkaido University
• Principal Investigator: Arai Asao 北海道大学, 理学研究院, 特任教授 (80134807)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: フォック空間 / 無限次元解析 / 無限次元デイラック作用素 / 無限次元ラプラシアン / 超対称性 / 超対称的量子場 / 時間作用素 / 正準交換関係と正準反交換関係の表現

Outline of Final Research Achievements

(1) An upper bound for the multiplicity of ground state of a class of quantum field models has been derived. (2) Detailed analyses have been done on in-equivalent representations of canonical commutation relations and canonical anti-commutation relations, which have physically important meanings. (3) For a general quantum system, a concept of ultra-weak time-operator has been introduced. Hierarchies of time-operators and their respective physical roles have been considered.

Free Research Field

数学