gauge fixing Lagrangian density

**algebraic quantum field theory** (perturbative, on curved spacetimes, homotopical)

**quantum mechanical system**, **quantum probability**

**interacting field quantization**

In BV-BRST formalism a *gauge fixing Lagrangian density* (traditionally called a “gauge fixing fermion”) is a Lagrangian density $\mathbf{L}_{gf}$ whose Lagrangian function $L_{gf}$ is in degree -1 in a resolved BV-BRST complex whose Hamiltonian flow under the local antibracket is used to isomorph the complex into one that admits a degreewise covariant phase space. This is part of the process of “gauge fixing” in BV-BRST formalism.

This is called a “fermion” only because it has to sit in BV-BRST degree (-1). Besides this odd grading, it has nothing to do with the concept of fermions. Of course, if the field theory in question does contain fermion fields, then the “gauge fixing fermion” may depend on these.

For details see at *A first idea of quantum field theory* the chapter *Gauge fixing*.

Last revised on December 14, 2017 at 12:42:18. See the history of this page for a list of all contributions to it.