A modification of the 10d superparticle action inspired by the Gupta-Bleuler quantization scheme method

TL;DR

This paper explores a modified superparticle action inspired by the Gupta-Bleuler quantization scheme, establishing a complex structure for the 10-dimensional superparticle that facilitates a consistent fermionic constraint splitting.

Contribution

It introduces a new Lagrangian formulation for the 10d superparticle that supports a holomorphic-antiholomorphic splitting aligned with Gupta-Bleuler quantization principles.

Findings

Proves the existence of a complex structure for the 10d superparticle.

Constructs an explicit Lagrangian enabling fermionic constraint splitting.

Ensures all first class constraints vanish on physical states.

Abstract

We reconsider the issue of the existence of a complex structure in the Gupta-Bleuler quantization scheme. We prove an existence theorem for the complex structure associated with the $d=10$ Casalbuoni-Brink-Schwarz superparticle, based on an explicitly constructed Lagrangian that allows a holomorphic-antiholomorphic splitting of the fermionic constraints consistent with the vanishing of all first class constraints on the physical states.