Quantization of the particle with a linear massless solution

• Published in: The journal of high energy physics 2018-11, Vol.2018 (11), p.1-19, Article 19
• Main Author: Jusinskas, Renann Lipinski
• Format: Article
• Language: English
• Subjects: BRST Quantization; Classical and Quantum Gravitation; Elementary Particles; First principles; Formalism; Gauge Symmetry; High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Superstrings and Heterotic Strings; Supersymmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2018)019

A bstract In this work, a solution linear in the momentum for the massless constraint P m P m = 0 is investigated. It is presented in terms of a SO(2 n , ℂ) to U( n ) decomposition and interpreted in terms of projective pure spinors, which are known to parametrize the SO 2 n U n coset. The worldline action is quantized using the BRST formalism and, using the results of Berkovits and Cherkis, the ghost number zero wave function is shown to generate massless solutions for field equations of arbitrary spin. The model can be covariantly expressed by the action recently proposed in D = 10 by Berkovits, in terms of a twistor-like constraint. However, a thorough account of its gauge symmetries does not lead to a spacetime supersymmetric theory. In order to derive from first principles the superparticle in the pure spinor formalism, a new model is proposed with partial worldline supersymmetry. The gauge algebra is then analyzed within the Batalin-Vilkovisky formalism and the gauge fixed action is finally shown to describe the pure spinor superparticle times a U(1) decoupled sector.