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On the scalar curvature for the noncommutative four torus / Farzad Fathizadeh; Farzad Fathi Zadeh

Journal of Mathematical Physics, Volume: 56, Issue: 6, Start page: 062303

Swansea University Author: Farzad, Fathi Zadeh

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DOI (Published version): 10.1063/1.4922815

Abstract

The canonical flat metric of the noncommutative four torus is conformally perturbed and the term corresponding to the scalar curvature in the heat kernel expansion of perturbed Laplacian is calculated by using an analog of the Wodziski residue. This allows the calculation to be done without using th...

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Published in: Journal of Mathematical Physics
ISSN: 0022-2488 1089-7658
Published: 2015
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URI: https://cronfa.swan.ac.uk/Record/cronfa40173
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Abstract: The canonical flat metric of the noncommutative four torus is conformally perturbed and the term corresponding to the scalar curvature in the heat kernel expansion of perturbed Laplacian is calculated by using an analog of the Wodziski residue. This allows the calculation to be done without using the so called rearrangement lemma. Thus, because of the simplicity of the method, the structure of the one and two variable of functions of a modular automorphism that appear in the formula for the curvature can be understood and functional relations among them are discovered. Also the gradient of the analog of the Einstein-Hilbert action is calculated explicitly, which prepares the ground for defining certain geometric flows (such as the Yamabe flow) on the noncommutative four torus.
College: College of Science
Issue: 6
Start Page: 062303