# BRST-BFV and BRST-BV Descriptions for Bosonic Fields with Continuous Spin on $R^{1,d-1}$

## TL;DR

This paper develops gauge-invariant, BRST-based formulations for free bosonic continuous spin fields in Minkowski space, providing both constrained and unconstrained descriptions, including Lagrangian and non-Lagrangian forms.

## Contribution

It introduces a comprehensive BRST-BFV and BRST-BV framework for continuous spin bosonic fields, unifying various formulations and deriving explicit equations of motion and Lagrangians.

## Key findings

- Constructed BRST-BFV equations with auxiliary fields
- Established equivalence with Poincare group conditions
- Derived unconstrained and constrained field formulations

## Abstract

Gauge-invariant descriptions for a free bosonic scalar field of continuous spin in a $d$-dimensional Minkowski space-time using a metric-like formulation are constructed on the basis of a constrained BRST-BFV approach we propose. The resulting BRST-BFV equations of motion for a scalar field augmented by ghost operators contains different sets of auxiliary fields, depending on the manner of a partial gauge-fixing and a resolution of some of the equations of motion for a BRST-unfolded first-stage reducible gauge theory. To achieve an equivalence of the resulting BRST-unfolded constrained equations of motion with the initial irreducible Poincare group conditions of a Bargmann--Wigner type, it is demonstrated that one should replace the field in these conditions by a class of gauge-equivalent configurations. Triplet-like, doublet-like constrained descriptions, as well as an unconstrained quartet-like non-Lagrangian and Lagrangian formulations, are derived using both Fronsdal-like and new tensor fields. In particular, the BRST--BV equations of motion and Lagrangian using an appropriate set of Lagrangian multipliers in the minimal sector of the respective field and antifield configurations are constructed in a manifest way.