Space-time symmetry and particle physics

2023 Fiscal Year Final Research Report

• Project/Area Number: 18K03633
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 15010:Theoretical studies related to particle-, nuclear-, cosmic ray and astro-physics
• Research Institution: Institute of Physical and Chemical Research
• Principal Investigator: FUJIKAWA Kazuo 国立研究開発法人理化学研究所, 数理創造プログラム, 客員研究員 (30013436)
• Project Period (FY): 2018-04-01 – 2024-03-31
• Keywords: quantum anomalies / Berry's phase / Majorana neutrinos

Outline of Final Research Achievements

The difference of quantum anomalies and the approximate Berry's phase has not been formulated in the past. The application of the adiabatic approximation to the exact quantum mechanical formulation leads to the adibatic Berry's phase.If the exact symmetry of the starting formulation can be realized in quantum theory only in a deformed form, it is generally defined as the quantum anomaly. A clear recognition of these differences would contribute to the precise description of the various applications of those field theoretical ideas in various fields of physics.
The recent analysis of the Majorana neutrinos in the seesaw mechanism in the Standard Model will force physicists to rewrite the descriptions in most textbooks and papers in neutrino physics. It is interesting that a Bogoliubov-like transformation is required to make a transition from the Weyl-type description to the Majorana description of neutrinos in quantum field theory.

Free Research Field

素粒子論

Academic Significance and Societal Importance of the Research Achievements

基礎物理学の考察が社会的な意義を持つかどうかは難しい問題であるが、われわれの行った量子異常とBerry位相の考察は素粒子論のみならず原子核物理学とか物性物理学等における量子論および場の理論の応用において重要になると予想される。
またMajoranaフェルミオンの考察は、通常のカイラルフェルミオンの考察と直行した角度からのスピノールの考察であり、将来のより明確な理解に導くものと考えられる。