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A Gutzwiller Trace formula for Dirac Operators on a Stationary Spacetime - MaRDI portal

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A Gutzwiller Trace formula for Dirac Operators on a Stationary Spacetime

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Publication:6378021

DOI10.1007/S12220-022-01084-XarXiv2109.09219MaRDI QIDQ6378021

Author name not available (Why is that?)

Publication date: 19 September 2021

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. extbf{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.





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