Superevolution

TL;DR

This paper explores a novel approach called superevolution in superspace, where supercharges govern state evolution, avoiding typical boson-fermion degeneracy, with applications in supersymmetric quantum mechanics and field theory.

Contribution

It introduces the concept of superevolution, providing an alternative to the Schrödinger equation in supersymmetric theories, and demonstrates its consistency and implications.

Findings

Superevolution is consistent with the Schrödinger equation.

It avoids degeneracy between bosonic and fermionic states.

Applicable to supersymmetric quantum mechanics and field theory.

Abstract

Usually, in supersymmetric theories, it is assumed that the time-evolution of states is determined by the Hamiltonian, through the Schr\"odinger equation. Here we explore the superevolution of states in superspace, in which the supercharges are the principal operators. The superevolution equation is consistent with the Schr\"odinger equation, but it avoids the usual degeneracy between bosonic and fermionic states. We discuss superevolution in supersymmetric quantum mechanics and in a simple supersymmetric field theory.