Orthosymplectically invariant functions in superspace

TL;DR

This paper introduces orthosymplectically invariant superfunctions, develops dimensional reduction theorems, and applies them to solve invariant Schrödinger equations and prove classical integral theorems in superspace.

Contribution

It defines spherically symmetric superfunctions in superspace and establishes new reduction theorems, enabling solutions to invariant quantum problems and proofs of classical theorems in this context.

Findings

Dimensional reduction theorems for superspace differentiation and integration

Solutions to orthosymplectically invariant Schrödinger equations

Proofs of Funk-Hecke and Bochner's theorems in superspace

Abstract

The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically symmetric functions can be used to solve orthosymplectically invariant Schroedinger equations in superspace, such as the (an)harmonic oscillator or the Kepler problem. Finally the obtained machinery is used to prove the Funk-Hecke theorem and Bochner's relations in superspace.