On the Structure of the $N=4$ Supersymmetric Quantum Mechanics in $D=2$ and $D=3$

TL;DR

This paper explores the structure of N=4 supersymmetric quantum mechanics in two and three dimensions, analyzing its superfield formulation, classical Lagrangian, and quantum Hamiltonians, revealing how flat space Schrödinger equations emerge through unitary transformations.

Contribution

It provides a detailed superfield formulation and analysis of N=4 SQM in D=2 and D=3, highlighting the structure of quantum Hamiltonians and the transformation to flat space Schrödinger equations.

Findings

Classical Lagrangian describes motion in conformally flat metric with potential

Quantum Hamiltonians can be transformed to flat space Schrödinger equations

Analysis of Bose and Fermi sectors in 2D and 3D N=4 SQM

Abstract

The superfield formulation of two - dimensional $N=4$ Extended Supersymmetric Quantum Mechanics (SQM) is described. It is shown that corresponding classical Lagrangian describes the motion in the conformally flat metric with additional potential term. The Bose and Fermi sectors of two- and three-dimensional $N=4$ SQM are analyzed. The structure of the quantum Hamiltonians is such, that the usual Shr\"{o}dinger equation in the flat space arises after some unitary transformation, demonstrating the effect of transmutation of the coupling constant and the energy of the initial model in some special cases.