Dirac operators and local invariants on perturbations of Minkowski space

2024/12/17 by Nguyen Viet Dang, Dang, Nguyen Viet, András Vasy +3 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Operator Algebra Research #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.2412.12714

openalex publication_date 2024/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For small perturbations of Minkowski space, we show that the square of the Lorentzian Dirac operator P= -D² has real spectrum apart from possible poles in a horizontal strip. Furthermore, for ε>0 we relate the poles of the spectral zeta function density of P-iε to local invariants, in particular to the Lorentzian scalar curvature. The proof involves microlocal propagation and radial estimates in a resolved scattering calculus as well as high energy estimates in a further resolved classical-semiclassical calculus.

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