Year: 2021
Type: preprint
Abstract: A Duistermaat-Guillemin-Gutzwiller trace formula for Dirac-type operators on a globally hyperbolic spatially compact stationary spacetime is achieved by generalising the recent construction by A. Strohmaier and S. Zelditch [Adv. Math. \textbf{376}, 107434 (2021)] to a vector bundle setting. We have analysed the spectrum of the Lie derivative with respect to a global timelike Killing vector field on the solution space of the Dirac equation and found that it consists of discrete real eigenvalues. The distributional trace of the time evolution operator has singularities at the periods of induced Killing flow on the space of lightlike geodesics. This gives rise to the Weyl law asymptotic at the vanishing period.
Source: arXiv (Cornell University)
Author: Islam, Onirban
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4286971283