Superprojectors in D=10

TL;DR

This paper classifies all massive irreducible super Poincaré representations in ten dimensions, introduces new Casimir operators, and develops superprojectors to aid in superparticle quantization.

Contribution

It provides a complete classification of massive super Poincaré representations in D=10 and introduces new Casimir operators and superprojectors for their analysis.

Findings

New Casimir operators fully specify super Poincaré representations.

A scalar superfield contains three irreducible massive supersymmetry representations.

Superprojectors are constructed and applied to superparticle quantization.

Abstract

We classify all massive irreducible representations of super Poincar\'e in D=10. New Casimir operators of super Poincar\'e are presented whose eigenvalues completely specify the representation. It is shown that a scalar superfield contains three irreducible representations of massive supersymmetry and we find the corresponding superprojectors. We apply these new tools to the quantization of the massive superparticle and we show that it must be formulated in terms of a superfield $B_\mn$ satisfying an adequate covariant restriction.