Generalised scalar particle quantisation in 1+1 dimensions and $D(2,1;\alpha)$

TL;DR

This paper explores the algebraic structure of the exceptional superalgebra D(2,1;α) in two dimensions, proposing a novel interpretation as a BRST quantisation superalgebra, and constructs related classical and quantum models.

Contribution

It introduces an alternative interpretation of D(2,1;α) as a BRST quantisation superalgebra and develops a superfield realization with a corresponding classical action.

Findings

Superfield realization of the algebra

Identification of physical states via BRST cohomology

Classical action and equations of motion derived

Abstract

The exceptional superalgebra $\D21a$ has been classified as a candidate conformal supersymmetry algera in two dimensions. We propose an alternative interpretation of it as an extended BFV-BRST quantisation superalgebra in 2D ($D(2,1;1) \simeq osp(2,2|2)$). A superfield realization is presented wherein the standard extended phase space coordinates can be identified. The physical states are studied via the cohomology of the BRST operator. Finally we reverse engineer a classical action corresponding to the algebraic model we have constructed, and identify the Lagrangian equations of motion.