Curing the Infinite Ghost Tower in 4d Siegel Superparticle

TL;DR

This paper presents an alternative method to harmonic superspace for quantizing the 4d Siegel superparticle, effectively canceling the infinite ghost tower and providing an explicit Lagrangian formulation with standard spin-statistics relations.

Contribution

It introduces a new approach that avoids harmonic superspace, cancels the infinite ghost tower via auxiliary variables, and maintains explicit Lagrangian and spin-statistics consistency.

Findings

The theory is of rank two after BRST treatment.

The new method matches previous results from harmonic superspace.

An explicit Lagrangian formulation is achieved.

Abstract

On an explicit example of the Siegel superparticle we study an alternative to the harmonic superspace approach. The latter seems to be the only method for quantizing infinitely reducible first class constraints currently available. In an appropriately extended phase space, the infinite ghost tower is effectively canceled by that coming from the sector of auxiliary variables. After a proper BRST treatment the theory proves to be of rank two which correlates well with the results obtained earlier within the framework of the harmonic superspace approach. The advantage of the novel technique, however, is the existence of an explicit Lagrangian formulation and the standard spin--statistics relations which hold for all the variables involved.