Supersymmetric Quantum Fields via Quantum Probability

Abstract

The super version of imprimitivity theorem is available now to describe global supersymmetry of systems using the representations of super Lie groups (SLG). This result uses the equivalence between super Harish- Chandra pairs and super Lie groups at the categorigal level and is applicable to super Poincare group and generalizes a smooth SI to super context. We apply the result to build supersymmetric quantum fields. Towards this end, we set up a super fock space of a disjoint union of super Hilbert spaces which is equivalent to super tensoring of boson (even) part symmetrically and that of fermion (odd) part antisymmetrically of the super particle Hilbert space. This leads to a super fock space that is disjoint union of bosonic and fermionic spaces, that is Z2 graded. We derive covariant Weyl operators for light-like fields, with the massless super spinorial multiplet as an illustrative example. First, we build a representation of a light-like little group in terms of Weyl operators. We then use this construction to induce a representation of Poincare group to construct the fields via super version of imprimitivity theorem.