On Parasupersymmetries and Relativistic Descriptions for Spin one Particles: II. The Interacting Context with (Electro)Magnetic Fields

Abstract

This second part belongs to a series of two papers devoted to a constructive review of the relativistic wave equations for vector mesons due to the recent impact of spin one developments in connection with parasupersymmetric quantum mechanics. Here, the mesons are interacting with external (electro)magnetic fields but the simplest context of homogeneous constant magnetic fields directed along the z‐axis is particularly studied. Discussions on reality of energy eigenvalues, on causal propagation and on gyromagnetic ratios are especially presented. Supersymmetries and parasupersymmetries are analysed with respect to new pseudosupersymmetries suggested by these developments in one particular context.

Matrix superpotentials and superintegrable systems for arbitrary spin

“…Let us remind that a nonlinear generalization of the Pauli interaction is requested also in the relativistic description of spin-one particle interacting with the constant magnetic field [15].…”

Cλ-extended harmonic oscillator and (para) supersymmetric quantum mechanics

“…Possible connections with other extensions of SSQM than PSSQM are also worth investigating. Realizations of pseudosupersymmetric [28] and orthosupersymmetric [29] quantum mechanics are under current study, and we hope to report on them in a near future.…”

Para, Pseudo, and Orthosupersymmetric Quantum Mechanics and their Bosonization

“…Pseudosupersymmetric quantum mechanics (pseudoSSQM) was introduced by Beckers, Debergh, and Nikitin [4,5] in a study of relativistic vector mesons interacting with an external constant magnetic field. In the nonrelativistic limit, their theory leads to a pseudosupersymmetric oscillator Hamiltonian, which can be realized in terms of mutually commuting boson and pseudofermion operators, where the latter are intermediate between standard fermion and p = 2 parafermion operators.…”

“…It is then possible to formulate a pseudoSSQM [4,5], characterized by a pseudosupersymmetric Hamiltonian H and pseudosupercharge operators Q, Q † , satisfying the relations…”

“…They can be realized in terms of bosons and parafermions [7], pseudofermions [4,5], or orthofermions [8], respectively.…”