A Remark on Schwarz's Topological Field Theory
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Applied mathematics, Particles and fields physics
The standard evaluation of the partition function $Z$ of Schwarz's topological field theory results in the Ray--Singer analytic torsion. Here we present an alternative evaluation which results in Z=1. Mathematically, this amounts to a novel perspective on analytic torsion: it can be formally written as a ratio of volumes of spaces of differential forms which is formally equal to 1 by Hodge duality. An analogous result for Reidemeister combinatorial torsion is also obtained.
Adams, D.H., & Prodanev, E. (2000). A Remark on Schwarz's Topological Field Theory. Letters in Mathematical Physics, vol. 51, no. 4. doi:10.1023/A:1007628622454