Ghost constraints and the covariant quantization of the superparticle in ten dimensions

TL;DR

This paper introduces a covariant quantization method for the superparticle in ten dimensions by modifying the Berkovits approach, enabling calculation of matrix elements despite pure spinor constraints.

Contribution

It presents a novel covariant quantization framework that lifts pure spinor constraints via BRST cohomology, including ghosts for ghosts, allowing matrix element computations.

Findings

Successfully quantized the superparticle covariantly

Calculated matrix elements of physical operators

Handled reducible pure spinor constraints with ghosts for ghosts

Abstract

We present a modification of the Berkovits superparticle. This is firstly in order to covariantly quantize the pure spinor ghosts, and secondly to covariantly calculate matrix elements of a generic operator between two states. We proceed by lifting the pure spinor ghost constraints and regaining them through a BRST cohomology. We are then able to perform a BRST quantization of the system in the usual way, except for some interesting subtleties. Since the pure spinor constraints are reducible, ghosts for ghosts terms are needed, which have so far been calculated up to level 4. Even without a completion of these terms, we are still able to calculate arbitrary matrix elements of a physical operator between two physical states.