DYNAMICAL RESIDUES OF LORENTZIAN SPECTRAL ZETA FUNCTIONS

被引：1

作者：

Nguyen Viet Dang ^{[1
]}

Wrochna, Miehal ^{[2
]}

机构：

[1] Univ Paris, Sorbonne Univ, Inst Math Jussieu, 4 Pl Jussieu, F-75252 Paris, France

[2] CY Cergy Paris Univ, Lab Anal Geometrie Modelisat, 2 Av Adolphe Chauvin, F-95302 Cergy Pontoise, France

来源：

JOURNAL DE L ECOLE POLYTECHNIQUE-MATHEMATIQUES | 2022年 / 9卷

关键词：

Guillemin– Wodzicki residue; spectral zeta functions; wave equation; Hadamard para-metrix; Pollicott-Ruelle resonances; QUANTUM-FIELD-THEORY; PSEUDODIFFERENTIAL-OPERATORS; FEYNMAN PROPAGATOR; RENORMALIZATION; MANIFOLDS; INTEGRALS; FORMULA; SPACE;

D O I：

10.5802/jep.205

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define a dynamical residue which generalizes the Guillemin-Wodzicki residue density of pseudo-differential operators. More precisely, given a Schwartz kernel, the definition refers to Pollicott-Ruelle resonances for the dynamics of scaling towards the diagonal. We apply this formalism to complex powers of the wave operator and we prove that residues of Lorentzian spectral zeta functions are dynamical residues. The residues are shown to have local geometric content as expected from formal analogies with the Riemannian case.

引用

页码：1245 / 1292

页数：49

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