2025/09/04 by Yan Yau Cheng, Cheng, Yan Yau
Mathematics · #math.NT #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.2509.04540
We show that an arithmetic path integral over the ℓ-torsion of a Jacobian J[ℓ] is equal to the trace of the Frobenius action on a representation of the Heisenberg group H(J[ℓ]), 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.