From Scattering Problems in Quantum Mechanics to Correlation Functions in Conformal Field Theory

2016 Fiscal Year Final Research Report

• Project/Area Number: 15H06641
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Particle/Nuclear/Cosmic ray/Astro physics
• Research Institution: Nihon University
• Principal Investigator: OHYA Satoshi 日本大学, 理工学部, 助手 (40755542)
• Project Period (FY): 2015-08-28 – 2017-03-31
• Keywords: 共形代数 / 繋絡作用素

Outline of Final Research Achievements

I have proposed a new Lie-algebraic approach to compute momentum-space two-point functions of conformal field theory (CFT) at finite temperature in any spacetime dimension d(>2). The keys to this proposal are the Unruh effect and intertwining operator. First, I have revisited thermalization of CFT by the Unruh effect and presented a systematic construction of thermal CFT in terms of the embedding space formalism. Second, I have shown that in thermal CFT the intertwining relations reduce to certain linear recurrence relations for two-point functions in the complex momentum space. These recurrence relations are nothing but the conformal Ward-Takahashi identities at finite temperature. It has been shown that all the momentum-space two-point functions are obtained by solving these recurrence relations.

Free Research Field

素粒子論