Tractable gauge-fixed BRST variational prescription

Develop a tractable gauge-fixing prescription for variational methods that generate mean-field solutions within the BRST framework, while preserving consistent symmetry restoration.

Background

The paper establishes that a BRST energy functional can reproduce the variation-after-projection result when the BRST construction is treated exactly and gauge fixing is handled consistently. However, applying gauge fixing directly within the variational method used to obtain mean-field solutions is substantially more difficult than performing projection or solving the constraint. The authors identify the absence of a tractable gauge-fixing prescription as an unresolved issue, motivating later discussion of possible parametrizations, Trotterization, and controlled Baker–Campbell–Hausdorff expansions.

Resolving this problem would enable BRST symmetry restoration to be incorporated directly into practical variational and mean-field calculations without relying on a separate projection integral, while retaining compatibility with approximation schemes and effective-field-theory power counting.

References

Still to be explored is the potential for gauge fixing, which can be done consistently by extending the Hamiltonian via a BRST-exact term. Gauge-fixing is non-trivial for the variational method that yields mean-field solutions, and a tractable prescription for doing so is, at this time, unclear.

— BRST quantization for the restoration of broken symmetries: a pedagogical example  (2609.10172 - Sharma et al., 9 Sep 2026) in Section 5.2, subsection “BRST symmetry and VAP” (immediately before subsection “Alternative parametrization of a BRST extension”)