Explicit Construction of the BRST Charge for W_4

TL;DR

This paper explicitly constructs the BRST charge for the W_4 algebra in different bases, aiding in the understanding of its algebraic structure and potential applications in theoretical physics.

Contribution

It provides explicit formulas for the BRST charge of W_4 in primary and quadratic bases, which was previously not fully detailed.

Findings

Explicit BRST charge formulas for W_4 algebra

Clarification of algebraic basis choices

Facilitation of further theoretical developments

Abstract

We give the explicite form of the BRST charge Q for the algebra W_4=WA_3 in the basis where the spin-3 and the spin-4 field are primary as well as for a basis where the algebra closes quadratically.