THE SUPERFIELD QUANTISATION OF A SUPERPARTICLE ACTION WITH AN EXTENDED LINE ELEMENT

Abstract

A massive superparticle action based on the generalised line element in N = 1 global superspace is quantised canonically. A previous method of quantising this action, based on a Fock space analysis, showed that states existed in three supersymmetric multiplets, each of a different mass. The quantisation procedure presented uses the single first class constraint as an operator condition on a general N = 1 superwavefunction. The constraint produces coupled equations of motion for the component wavefunctions. Transformations of the component wavefunctions are derived that decouple the equations of motion and partition the resulting wavefunctions into three separate supermultiplets. Unlike previous quantisations of superparticle actions in N = 1 global superspace, the spinor wavefunctions satisfy the Dirac equation and the vector wavefunctions satisfy the Proca equation. The off-shell closure of the commutators of the supersymmetry transformations, that include mass parameters, are derived by the introduction of auxiliary wavefunctions. To avoid the ghosts arising in a previous Fock space quantisation an alternative conjugation is used in the definition of the current, based on a Krein space approach.