Formulation to quantize gauge field theories in physics
In theoretical physics, the BRST formalism, or BRST quantization (where the BRST refers to the last names of Carlo Becchi, Alain Rouet, Raymond Stora and Igor Tyutin) denotes a relatively rigorous mathematical approach to quantizing a field theory with a gauge symmetry. Quantization rules in earlier quantum field theory (QFT) frameworks resembled "prescriptions" or "heuristics" more than proofs, especially in non-abelian QFT, where the use of "ghost fields" with superficially bizarre properties is almost unavoidable for technical reasons related to renormalization and anomaly cancellation.
The BRST global supersymmetry introduced in the mid-1970s was quickly understood to rationalize the introduction of these Faddeev–Popov ghosts and their exclusion from "physical" asymptotic states when performing QFT calculations. Crucially, this symmetry of the path integral is preserved in loop order, and thus prevents introduction of counterterms which might spoil renormalizability of gauge theories. Work by other authors [by whom? – Discuss] a few years later related the BRST operator to the existence of a rigorous alternative to path integrals when quantizing a gauge theory.
Only in the late 1980s, when QFT was reformulated in fiber bundle language for application to problems in the topology of low-dimensional manifolds (topological quantum field theory), did it become apparent that the BRST "transformation" is fundamentally geometrical in character. In this light, "BRST quantization" becomes more than an alternate way to arrive at anomaly-cancelling ghosts. It is a different perspective on what the ghost fields represent, why the Faddeev–Popov method works, and how it is related to the use of Hamiltonian mechanics to construct a perturbative framework. The relationship between gauge invariance and "BRST invariance" forces the choice of a Hamiltonian system whose states are composed of "particles" according to the rules familiar from the canonical quantization formalism. This esoteric consistency condition therefore comes quite close to explaining how quanta and fermions arise in physics to begin with.
In certain cases, notably gravity and supergravity, BRST must be superseded by a more general formalism, the Batalin–Vilkovisky formalism.
In theoretical physics, the BRST formalism, or BRSTquantization (where the BRST refers to the last names of Carlo Becchi, Alain Rouet, Raymond Stora and...
finding the global optimum of black box functions BRSTquantization in Yang-Mills theories, a way to quantize a gauge-symmetric field theory Brasília Summer...
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context, it is also called the second quantization of fields, in contrast to the semi-classical first quantization of single particles. When it was first...
counterterms motivated by anomaly cancellation, in an approach known as BRSTquantization. While these concerns are in one sense highly technical, they are...
rigorous generalization of the Faddeev–Popov procedure is given by BRSTquantization.: 517 Spontaneous symmetry breaking is a mechanism whereby the symmetry...
light-front quantization of quantum field theory models, string theory models and D-brane actions using the Hamiltonian, path integral and BRSTquantization methods...
various ways to quantize the string within this framework including light-cone quantization, old canonical quantization, and BRSTquantization. A consistent...
some formulations of quantum field theory, in particular, canonical quantization in the interaction picture. In other formulations, the same event is...
in the quantum mechanical sense, becomes more evident in the BRST formalism of quantization. In any non-abelian gauge theory, any maximal abelian gauge...
field in question. The second quantization of quantum field theory requires that each such ball-spring combination be quantized, that is, that the strength...
up using Klein transformations. See parastatistics and also the ghosts in BRST. The impossibility of superluminal communication – if two observers are spacelike...
Goldstone bosons, that are removed in the latter case due to gauge freedom. Quantization preserves this gauge freedom property. A quartic massless scalar field...
zero-point field is sometimes used as a synonym for the vacuum state of a quantized field which is completely individual.[clarification needed] According...
with coining the term "quantum electrodynamics". Dirac described the quantization of the electromagnetic field as an ensemble of harmonic oscillators with...
Verlag. ISBN 9783540875604. Greiner, W.; Reinhardt, J. (1996). Field Quantization. Springer Verlag. ISBN 9783540591795. Griffiths, D. J. (1987). Introduction...
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