Junker, G. Supersymmetry of Relativistic Hamiltonians for Arbitrary Spin. Symmetry2020, 12, 1590.
Junker, G. Supersymmetry of Relativistic Hamiltonians for Arbitrary Spin. Symmetry 2020, 12, 1590.
Hamiltonians describing the relativistic quantum dynamics of a particle with an arbitrary spin are shown to exhibit a supersymmetric structure when the even and odd elements of the Hamiltonian commute. For such supersymmetric Hamiltonians an exact Foldy-Wouthuysen transformation exits which brings it into a block-diagonal form separating the positive and negative energy subspaces. Here the supercharges transform between energy eigenstates of positive and negative energy. The relativistic dynamics of a charged particle in a magnetic field is considered for the case of a scalar (spin-zero) boson obeying the Klein-Gordan equation, a Dirac (spin one-half) fermion and a vector (spin-one) boson characterised by the Proca equation.
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.