BRST Symmetry Transformations in Gauge Theories

BRST symmetry transformations furnish a coherent framework for quantising gauge theories while preserving underlying invariances. At their core, these transformations introduce anticommuting ghost fields and implement gauge fixing through a nilpotent operator that encodes the original gauge symmetry in a cohomological language. The construction ensures that physical observables reside in the cohomology of the BRST charge, thereby guaranteeing gauge independence of the S-matrix. Beyond the standard formulation, extensions such as anti-BRST and finite field-dependent BRST (FFBRST) transformations have been developed to relate different gauge choices and to probe non-perturbative regimes. These methods have found application in quantum chromodynamics, gravitational models and topological field theories, where the interplay between ghosts, gauge fixing and field redefinitions can elucidate phenomena such as confinement, anomaly cancellation and duality. Recent advances continue to deepen our understanding of the consistency conditions required for generalised BRST algebras and their implementations in superspace or higher-derivative contexts.

Research from Nature Portfolio

No recent Nature Portfolio content available.

BRST Symmetry Transformations in Gauge Theories publication trend

The graph below shows the total number of articles in brst symmetry transformations in gauge theories across all publications each year (not limited to Nature Index journals).

Technical terms

Gauge theory: A field theory whose dynamics are invariant under local transformations of an internal symmetry group.

BRST transformation: A symmetry operation combining gauge variation with ghost-field shifts, generated by a nilpotent operator that enforces gauge invariance at the quantum level.

Ghost fields: Anticommuting scalar fields introduced in the path integral to compensate for overcounting of gauge configurations and to ensure unitarity and renormalisability.

Nilpotency: The property of an operator whose square vanishes (Q^2=0), which underlies the cohomological classification of physical states in BRST quantisation.

Finite field-dependent BRST transformation: A generalisation of the standard BRST symmetry in which transformation parameters depend on the fields themselves, allowing for mappings between different gauge-fixed actions.

References

1. Non-perturbative to perturbative QCD via the FFBRST. European Physical Journal C (2018).
2. Search for Abelian dominance in the effective SO(N) theory. Physics Letters B (2019).
3. Superspace formulation with a new and extended BRST. Physics Letters B (2019).