A Trace-Path Integral Formula over Function Fields

Abstract

We show that an arithmetic path integral over the $\ell$-torsion of a Jacobian $J[\ell ]$ is equal to the trace of the Frobenius action on a representation of the Heisenberg group $H(J[\ell ])$, up to an explicitly determined sign. This is an arithmetic analogue of trace--path integral formulae which arise in quantum field theory, where path integrals over a space of sections of a fibration over a circle can be expressed as the trace of the monodromy action on a Hilbert space.

32 pages. To appear in the Journal of the London Mathematical Society

References in corpus (1)

• Quantization of Kähler manifolds