Extended BRST symmetries. Quantum approach

TL;DR

This paper explains the extension of BRST symmetries to quantum systems, including larger symmetries like sp(2), and illustrates the approach with a nonlinear system example.

Contribution

It introduces a quantum approach to extended BRST symmetries, detailing how classical structures are generalized and applied to complex systems.

Findings

Extended BRST symmetries are formulated at the quantum level.

The approach includes larger symmetries such as sp(2).

Application to a nonlinear system with open superalgebra demonstrates the method.

Abstract

The aim of this lecture is to present in a comprehensible way what the BRST quantization means and how the "classical" master equation, action and BRST transformations have to be prolonged towards the same "quantum" items. The presentation will focus not only on the standard BRST symmetry, but on larger symmetries as sp(2), both in the Lagrangean and in the Hamiltonian formalisms. How to find answers to these questions in more sophisticated cases will be illustrated by the example of a nonlinear system with open superalgebra.