Riemann-Roch-Hirzebruch theorem and Topological Quantum Mechanics

Details Riemann-Roch-Hirzebruch theorem and Topological Quantum Mechanics Riemann-Roch-Hirzebruch theorem and Topological Quantum Mechanics

2004-01-28

arxiv.org/abs/math/0401400v1

Mathematics

Quantum Algebra

24 pages, no figures, LaTeX

Scientific paper

In the present paper we discuss an independent on the Grothendieck-Sato isomorphism approach to the Riemann-Roch-Hirzebruch formula for an arbitrary differential operator. Instead of the Grothendieck-Sato isomorphism, we use the Topological Quantum Mechanics (more or less equivalent to the well-known constructions with the Massey operations from [KS], [P], [Me]). The statement that the Massey operations can "produce" the integral in some set-up, has an independent from the RRH theorem interest. We finish the paper by some open questions arising when the main construction is applied to the cyclic homology (instead of the Hochschild homology).

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