On Certain Spectral Invariants of Dirac Operators on Noncommutative Tori

2015/04/05 by Ali Fathi, Fathi, Ali, Masoud Khalkhali +1 · 2 citations
Mathematics · Physics and Astronomy · #46L87 #58B34 #58J42 #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Algebra (math.QA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1504.01174

openalex publication_date 2015/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The spectral eta function for certain families of Dirac operators on noncommutative 3-torus is considered and the regularity at zero is proved. By using variational techniques, we show that η_D(0) is a conformal invariant. By studying the Laurent expansion at zero of TR (|D|^-z), the conformal invariance of ζ'_|D|(0) for noncommutative 3-torus is proved. Finally, for the coupled Dirac operator, a local formula for the variation ∂_Aη_D+A(0) is derived which is the analogue of the so called induced Chern-Simons term in quantum field theory literature.

Citations

• The Gauss-Bonnet Theorem for the noncommutative two torus

Cited by

• Pseudodifferential calculus on noncommutative tori, I. Oscillating integrals
• A Scalar Curvature Formula For the Noncommutative 3-Torus

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