DOI: 10.1112/jlms.70664 ISSN: 0024-6107
A trace–path integral formula over function fields
Yan Yau ChengAbstract
We show that an arithmetic path integral over the ‐torsion of a Jacobian is equal to the trace of the Frobenius action on a representation of the Heisenberg group , 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.