Integration on Non-Compact Supermanifolds

TL;DR

This paper develops a general Stokes's theorem for non-compact supermanifolds with corners, providing explicit boundary term representations for Berezin integrals under variable changes, including high-order derivatives.

Contribution

It introduces a coordinate-free, explicit formula for boundary terms in Berezin integrals on non-compact supermanifolds with corners, extending Stokes's theorem.

Findings

Derived a general Stokes's theorem for supermanifolds with corners.

Provided explicit boundary term formulas involving high-order derivatives.

Extended the understanding of Berezin integrals in non-compact settings.

Abstract

We investigate the Berezin integral of non-compactly supported quantities. In the framework of supermanifolds with corners, we give a general, explicit and coordinate-free repesentation of the boundary terms introduced by an arbitrary change of variables. As a corollary, a general Stokes's theorem is derived - here, the boundary integral contains transversal derivatives of arbitrarily high order.