Becky-Rouet-Stora-Tyutin quantization method

The Becky – Rouet – Stora – Tyutin quantization method ( BRST quantization ) is a theoretical physics method that uses a rigorous approach to quantizing field theory in the presence of gauge symmetry . Named after Carlo Becchi ( Eng. Carlo Becchi ), Alain Rouet ( Alain Rouet ), Raymond Stora ( French Raymond Stora ) and Igor Tyutin .

The quantization rules in the early methods of quantum field theory were more a set of practical heuristics (“recipes”) than a strict system. This is especially true for the case of non-Abelian gauge theories , where the use of " Faddeev-Popov spirits " with bizarre properties is simply necessary for some technical reasons related to renormalization and incorrect reduction.

BRST supersymmetry was invented in the mid-1970s and was quickly accepted by the community as a way of rigorous justification for introducing the Faddeev – Popov spirits and their exclusion from physical asymptotics in calculations. A few years later in the work of another author ^{[ clarify ] it} was shown that the BRST operator indicates the existence of a formal alternative to the path integral in quantizing the gauge theory.

Only in the late 1980s was it ready, when quantum field theory was formulated in terms of bundles for the possibility of solving topological problems of low-dimensional manifolds (Donaldson theory), it became obvious that the nature of the BRST transformation is fundamentally geometric. In this light, “BRST quantization” is not just a way to achieve abnormally contracting spirits. ^{[ specify ]} . This is a different view of what perfume fields are, why the Faddeev-Popov method is valid, and how it is associated with the use of Hamiltonian mechanics in constructing a perturbation model. The correlation between gauge invariance and “BRST invariance” limits the choice of Hamiltonian systems whose states consist of “particles” in accordance with the rules of canonical quantization . This implicit consistency comes quite close to explaining where quanta and fermions come from in physics.

In certain cases, in particular in the theories of gravity and supergravity , BRST quantization should be replaced by the more general Batalin-Vilkovsky formalism .