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- BRST_quantization abstract "In theoretical physics, BRST quantization (where the BRST refers to Becchi, Rouet, Stora and Tyutin) denotes a relatively rigorous mathematical approach to quantizing a field theory with a gauge symmetry. Quantization rules in earlier 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 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, 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how quanta and fermions arise in physics to begin with.In certain cases, notably gravity and supergravity, BRST must be superseded by a more general formalism, the Batalin–Vilkovisky formalism.".
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- BRST_quantization wikiPageWikiLink Abelian_gauge_theory.
- BRST_quantization wikiPageWikiLink Action_(physics).
- BRST_quantization wikiPageWikiLink Action_functional.
- BRST_quantization wikiPageWikiLink Action_principle.
- BRST_quantization wikiPageWikiLink Active_and_passive_transformation.
- BRST_quantization wikiPageWikiLink Adiabatic_theorem.
- BRST_quantization wikiPageWikiLink Anomaly_(physics).
- BRST_quantization wikiPageWikiLink Anomaly_cancellation.
- BRST_quantization wikiPageWikiLink Antiderivation.
- BRST_quantization wikiPageWikiLink Asymptotic_freedom.
- BRST_quantization wikiPageWikiLink Automorphism.
- BRST_quantization wikiPageWikiLink Auxiliary_field.
- BRST_quantization wikiPageWikiLink Batalin–Vilkovisky_formalism.
- BRST_quantization wikiPageWikiLink Bryce_DeWitt.
- BRST_quantization wikiPageWikiLink C-number.
- BRST_quantization wikiPageWikiLink Canonical_quantization.
- BRST_quantization wikiPageWikiLink Carlo_Becchi.
- BRST_quantization wikiPageWikiLink Category:Cohomology_theories.
- BRST_quantization wikiPageWikiLink Category:Quantum_chromodynamics.
- BRST_quantization wikiPageWikiLink Category:Quantum_field_theory.
- BRST_quantization wikiPageWikiLink Chain_complex.
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- BRST_quantization wikiPageWikiLink Classical_electromagnetism.
- BRST_quantization wikiPageWikiLink Closed_and_exact_differential_forms.
- BRST_quantization wikiPageWikiLink Closed_differential_form.
- BRST_quantization wikiPageWikiLink Cochain_complex.
- BRST_quantization wikiPageWikiLink Cohomology.
- BRST_quantization wikiPageWikiLink Collider.
- BRST_quantization wikiPageWikiLink Color_confinement.
- BRST_quantization wikiPageWikiLink Connection_(principal_bundle).
- BRST_quantization wikiPageWikiLink Connection_form.
- BRST_quantization wikiPageWikiLink Conserved_charge.
- BRST_quantization wikiPageWikiLink Constraint_equation.
- BRST_quantization wikiPageWikiLink Continuum_electrodynamics.
- BRST_quantization wikiPageWikiLink Coordinate_system.
- BRST_quantization wikiPageWikiLink Coupling_constant.
- BRST_quantization wikiPageWikiLink Covariant_derivative.
- BRST_quantization wikiPageWikiLink Definite_bilinear_form.
- BRST_quantization wikiPageWikiLink Definite_quadratic_form.
- BRST_quantization wikiPageWikiLink Derivation_(differential_algebra).
- BRST_quantization wikiPageWikiLink Differential_geometry.
- BRST_quantization wikiPageWikiLink Dimensional_regularization.
- BRST_quantization wikiPageWikiLink Dirac_picture.
- BRST_quantization wikiPageWikiLink Donaldson_theory.
- BRST_quantization wikiPageWikiLink Dyson_series.
- BRST_quantization wikiPageWikiLink Edward_Witten.
- BRST_quantization wikiPageWikiLink Effective_field_theories.
- BRST_quantization wikiPageWikiLink Effective_field_theory.
- BRST_quantization wikiPageWikiLink Eigenvalue.
- BRST_quantization wikiPageWikiLink Eigenvalues_and_eigenvectors.
- BRST_quantization wikiPageWikiLink Electromagnetic_four-potential.
- BRST_quantization wikiPageWikiLink Electroweak_interaction.
- BRST_quantization wikiPageWikiLink Electroweak_theory.
- BRST_quantization wikiPageWikiLink Elsevier.
- BRST_quantization wikiPageWikiLink Energy.
- BRST_quantization wikiPageWikiLink Equivalence_class.
- BRST_quantization wikiPageWikiLink Equivalence_classes.
- BRST_quantization wikiPageWikiLink Exact_form.
- BRST_quantization wikiPageWikiLink Exterior_calculus.
- BRST_quantization wikiPageWikiLink Exterior_derivative.
- BRST_quantization wikiPageWikiLink Faddeev–Popov_ghost.
- BRST_quantization wikiPageWikiLink Faddeev–Popov_ghosts.
- BRST_quantization wikiPageWikiLink Fermion.
- BRST_quantization wikiPageWikiLink Fermions.
- BRST_quantization wikiPageWikiLink Fermi–Dirac_statistics.
- BRST_quantization wikiPageWikiLink Feynman_diagram.
- BRST_quantization wikiPageWikiLink Feynman_diagrams.
- BRST_quantization wikiPageWikiLink Feynman_path_integral.
- BRST_quantization wikiPageWikiLink Feynman_rules.
- BRST_quantization wikiPageWikiLink Fiber_bundle.
- BRST_quantization wikiPageWikiLink Field_operators.
- BRST_quantization wikiPageWikiLink First_class_constraint.
- BRST_quantization wikiPageWikiLink Fock_space.
- BRST_quantization wikiPageWikiLink Fock_state.
- BRST_quantization wikiPageWikiLink Four-potential.
- BRST_quantization wikiPageWikiLink Functional_determinant.
- BRST_quantization wikiPageWikiLink Functional_integral.
- BRST_quantization wikiPageWikiLink Functional_integration.
- BRST_quantization wikiPageWikiLink Functional_measure.
- BRST_quantization wikiPageWikiLink Functional_quantization.
- BRST_quantization wikiPageWikiLink Gauge_anomaly.
- BRST_quantization wikiPageWikiLink Gauge_bundle.
- BRST_quantization wikiPageWikiLink Gauge_fixing.
- BRST_quantization wikiPageWikiLink Gauge_group.
- BRST_quantization wikiPageWikiLink Gauge_invariance.