The supercharge and superconformal symmetry for N=1 supersymmetric quantum mechanics

TL;DR

This paper develops a superspace Lagrangian framework for N=1 supersymmetric quantum mechanics, exploring superconformal symmetry, deriving Noether charges, and analyzing Ward identities in a magnetic field context.

Contribution

It introduces a comprehensive superspace formulation for N=1 supersymmetric quantum mechanics, including superconformal generators and symmetry breaking analysis.

Findings

Constructed a general Lagrangian with chiral supercoordinates

Derived superconformal Ward identities for the effective action

Identified sources of symmetry breaking terms

Abstract

The superspace Lagrangian formulation of N=1 supersymmetric quantum mechanics is presented. The general Lagrangian constructed out of chiral and antichiral supercoordinates containing up to two derivatives and with a canonically normalized kinetic energy term describes the motion of a nonrelativistic spin 1/2 particle with Land\'e g-factor 2 moving in two spatial dimensions under the influence of a static but spatially dependent magnetic field. Noether's theorem is derived for the general case and is used to construct superspace dependent charges whose lowest components give the superconformal generators. The supercoordinate of charges containing an R symmetry charge, the supersymmetry charges and the Hamiltonian are combined to form a supercharge supercoordinate. Superconformal Ward identities for the quantum effective action are derived from the conservation equations and the source of potential symmetry breaking terms are identified.