Heat asymptotics for nonminimal Laplace type operators and application to noncommutative tori
Jul 30, 2017Citations per year
Abstract: (Elsevier)
Let P be a Laplace type operator acting on a smooth hermitean vector bundle V of fiber CN over a compact Riemannian manifold given locally by P=−[gμνu(x)∂μ∂ν+vν(x)∂ν+w(x)] where u,vν,w are MN(C) -valued functions with u(x) positive and invertible. For any a∈Γ(End(V)) , we consider the asymptotics Tr(ae−tP)∼t↓0+∑r=0∞ar(a,P)t(r−d)∕2 where the coefficients ar(a,P) can be written as an integral of the functions ar(a,P)(x)=tr[a(x)Rr(x)] .
The computation of R2 is performed opening the opportunity to calculate the modular scalar curvature for noncommutative tori.Note:
- 32 pages. v2: small modifications in the text, added the missing ancillary Mathematica notebook file which proves, by direct computations, some results established in the paper
- 58J35
- 35J47
- 81T13
- 46L87
- Heat kernel
- Nonminimal operator
- Asymptotic heat trace
- Laplace type operator
- Scalar curvature
- Noncommutative torus
References(28)
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