Supersymmetric Dynamics of a Spin-1/2 Particle in an Extended External Field

TL;DR

This paper explores the supersymmetric dynamics of a spin-1/2 particle in a five-dimensional external field, linking higher-dimensional energy flow to supersymmetry and symmetry breaking in nonrelativistic quantum mechanics.

Contribution

It introduces a novel supersymmetry framework derived from a five-dimensional Dirac equation and interprets the fifth dimension's energy as an extra electrical vector.

Findings

Identification of a supersymmetry sector in quantum dynamics

Definition of an extra electrical vector from the fifth dimension

Energy flow from the fifth dimension influences space symmetry

Abstract

We consider a electron in a external field in D=5, through the Dirac equation in the Galilean symmetry approach, and in the Lorentz symmetry approach; from these we perform the nonrelativistic limit, then we procede the supersymmetry of the same that is associated with the Galilean symmetry, we identify as a supersymmetry sector from the quantum-mechanical dynamics, and we got the algebra of fermionic charges. We naturally define as extra electrical vector E, and interpret the terms of energy coming from the fifth dimension. The energy from the fifth dimension, criate this extra electrical vector E, associated with the fifth component of the external electrical field A, this makes the energy flow from the fifth dimension to the usual three-dimensional space, when some symmetries of the usual space are broken, giving a preferential direction in the space, even though the standard electrical and magnetic fields are null.