A proposal for a generalized canonical osp(1,2) quantization of dynamical systems with constraints

TL;DR

This paper introduces a generalized osp(1,2)-based quantization method for dynamical systems with constraints, analyzing gauge dependence and establishing conditions for gauge independence in the quantization process.

Contribution

It proposes a new osp(1,2)-covariant quantization framework applicable to systems with first-class constraints, extending existing methods with a focus on gauge independence.

Findings

Gauge dependence of Green's functions when m^2 ≠ 0

Gauge independence restored as m → 0

Derived Ward identities for osp(1,2) symmetry

Abstract

The aim of this paper is to consider a possibility of constructing for arbitrary dynamical systems with first-class constraints a generalized canonical quantization method based on the osp(1,2) supersymmetry principle. This proposal can be considered as a counterpart to the osp(1,2)-covariant Lagrangian quantization method introduced recently by Geyer, Lavrov and M\"ulsch. The gauge dependence of Green's functions is studied. It is shown that if the parameter m^2 of the osp(1,2) superalgebra is not equal to zero then the vacuum functional and S-matrix depend on the gauge. In the limit $m\to 0$ the gauge independence of vacuum functional and S - matrix are restored. The Ward identities related to the osp(1,2) symmetry are derived.