Covariant Quantization of d=4 Brink-Schwarz Superparticle with Lorentz Harmonics

TL;DR

This paper develops a covariant quantization method for the d=4 superparticle using Lorentz harmonics, revealing the structure of massless superfields and their relation to spin, statistics, and infinite-component fields.

Contribution

It introduces a gauge auxiliary spinor Lorentz harmonic framework for covariant quantization of the superparticle and analyzes the properties of resulting superfields, including their reducibility and connection to Weinberg's theorem.

Findings

Superfields correspond to finite superspin representations.

Only harmonic fields with proper spin-statistics connection satisfy microcausality.

The approach generalizes Weinberg's theorem to infinite-component fields.

Abstract

Covariant first and second quantization of the free d=4 massless superparticle are implemented with the introduction of purely gauge auxiliary spinor Lorentz harmonics. It is shown that the general solution of the condition of maslessness is a sum of two independent chiral superfields with each of them corresponding to finite superspin. A translationally covariant, in general bijective correspondence between harmonic and massless superfields is constructed. By calculation of the commutation function it is shown that in the considered approach only harmonic fields with correct connection between spin and statistics and with integer negative homogeneity index satisfy the microcausality condition. It is emphasized that harmonic fields that arise are reducible at integer points. The index spinor technique is used to describe infinite-component fields of finite spin; the equations of motion of such fields are obtained, and for them Weinberg's theorem on the connection between massless helicity particles and the type of nongauge field that describes them is generalized.