nLab BV-Lagrangian density

Idea

In BV-BRST formalism the plain Lagrangian density $\mathbf{L}$ of a given Lagrangian field theory is accompanied by an auxiliary Lagrangian density $\mathbf{L}_{BRST}$ depending on auxiliary fields such as ghost fields and antifields, such that the local antibracket with the sum $-\mathbf{L} + \mathbf{L}_{BRST}$ yields the BV-BRST differential

$$s \;=\; \left\{ - \mathbf{L} + \mathbf{L}_{BRST} \,,\, - \right\}$$

which models the derived critical locus $\delta_{EL}\mathbf{L} \simeq 0$ inside the homotopy quotient modeled by the BRST complex of the theory.

Related concepts

• gauge fixing Lagrangian density