Heat trace for Laplacian type operators with non-scalar symbols

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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https://hal.archives-ouvertes.fr/hal-01347436
Contributeur : Thierry Masson <>
Soumis le : jeudi 21 juillet 2016 - 08:34:58
Dernière modification le : mardi 18 avril 2017 - 15:22:30

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Bruno Iochum, Thierry Masson. Heat trace for Laplacian type operators with non-scalar symbols. Journal of Geometry and Physics, Elsevier, 2017, 116, pp.90-118. 〈10.1016/j.geomphys.2017.01.014〉. 〈hal-01347436〉

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