Search for a/the correct framework(s) of quantum field theories

2021 Fiscal Year Final Research Report

• Project/Area Number: 17H04837
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Single-year Grants
• Research Field: Particle/Nuclear/Cosmic ray/Astro physics
• Research Institution: The University of Tokyo
• Principal Investigator: Tachikawa Yuji 東京大学, カブリ数物連携宇宙研究機構, 教授 (10639587)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: 場の量子論 / 数学的定式化

Outline of Final Research Achievements

Originally, I planned to start from the known formulation of two-dimensional quantum field theory using vertex operator algebras, and generalize it to higher-dimensional quantum field theories. Unfortunately this direction did not proceed as expected, and I decided to concentrate my efforts on generalizing and studying the concept of the symmetry and anomaly of quantum field theory. Luckily this direction was more successful. For example, in a paper from 2018 coauthored with Bhardwaj, I pointed out that symmetry operations, which were usually taken to be always invertible, can be generalized to non-invertible operations. This observation has slowly been taken up by researchers worldwide, and in particular, many papers studying this point further have appeared as preprints this year (2022).

Free Research Field

数理物理

Academic Significance and Societal Importance of the Research Achievements

場の量子論は我々を構成している素粒子の従う法則であるのみならず、超伝導や量子ホール効果などの物性理論においても基礎的であり、理論からの予測は実験とも良く合うことが知られている。しかしながら、場の量子論は数学的にキチンと理解されていない。例えていえば、古代エジプト人はピタゴラスの定理を実際上知っていて、ピラミッドを造れたが、ユークリッド幾何という定式化を知らなかったような状況である。ユークリッド幾何が古代ギリシャ以後の科学の進展に果たしたように、場の量子論を数学的に整備することは、人類の科学の長期的な理解に資すると考えられる。