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arXiv · 1607.06070

Heat trace for Laplacian type operators with non-scalar symbols

Bruno Iochum·Thierry Masson
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Abstract

For an elliptic selfadjoint operator $P =-[u^{\mu\nu}\partial_\mu \partial_\nu +v^\nu \partial_\nu +w]$ acting on a fiber bundle over a Riemannian manifold, where $u,v^\mu,w$ are $N\times N$-matrices, we develop a method to compute the heat-trace coefficients $a_r$ which allows to get them by a pure computational machinery. It is exemplified in dimension 4 by the value of $a_1$ written both in terms of $u,v^\mu,w$ or diffeomorphic and gauge invariants. We also answer to the question: when is it possible to get explicit formulae for $a_r$?

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BibTeXRIS

Bruno Iochum, Thierry Masson. 2016-07-20. Heat trace for Laplacian type operators with non-scalar symbols. https://doi.org/10.1016/j.geomphys.2017.01.014

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