BRST is an abbreviation for the Batalin, Fradkin, Vilkovisky and Tyutin formalism, which is a mathematical framework used in quantum field theory to treat the quantization of fields with gauge symmetry. This formalism was developed by Igor Batalin, Sergey Fradkin, Dimitri Vilkovisky, and Igor Tyutin in the 1970s.
In the BRST formalism, the gauge symmetry is treated as a global symmetry, allowing for a consistent quantization of the theory. It introduces additional degrees of freedom known as ghost fields and antighost fields, which cancel out the unphysical degrees of freedom associated with the gauge symmetry.
The ghost and antighost fields are fermionic, carrying half-integer spin, and interact with the original gauge fields. The BRST transformation is a nilpotent symmetry transformation that relates the gauge fields, ghost fields, and antighost fields.
This formalism is particularly important in the quantization of Yang-Mills theories, which describe the interactions of elementary particles through the fundamental forces. The BRST formalism provides a systematic way to compute scattering amplitudes and study the quantum properties of gauge theories.
Overall, the BRST formalism is a powerful tool in quantum field theory, allowing for the consistent quantization of gauge theories and providing a framework to study their properties at the quantum level.
