Recent Developments in Supersymmetric Quantum Mechanics

TL;DR

This paper reviews recent advances in supersymmetric quantum mechanics, introducing new semi-classical formulas, exploring implications for Pauli's Hamiltonian, and providing counterexamples to the paramagnetic conjecture.

Contribution

It presents novel semi-classical approximation formulas and explores the supersymmetric structure of Pauli's Hamiltonian, offering new insights and counterexamples.

Findings

New semi-classical approximation formulas for supersymmetric quantum mechanics

Supersymmetry in Pauli's Hamiltonian relates to a modified Witten's index

Counterexample to the paramagnetic conjecture based on supersymmetry

Abstract

Some recent results in supersymmetric quantum mechanics are presented. New semi-classical approximation formulas for Witten's realization of supersymmetric quantum mechanics are discussed. Implications of the supersymmetric structure of Pauli's Hamiltonian are also considered. In particular, the paramagnetisation of a non-interacting electron gas is related to a modified version of Witten's index. We also show that the supersymmetry in this system provides a new counter example for the paramagnetic conjecture.