Moyal bracket
E443157
bracket operation
concept in deformation quantization
concept in quantum mechanics
mathematical operation
The Moyal bracket is a mathematical operation in phase-space quantum mechanics that generalizes the classical Poisson bracket to describe quantum corrections in the evolution of quasiprobability distributions.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Moyal bracket canonical | 1 |
Statements (39)
| Predicate | Object |
|---|---|
| instanceOf |
bracket operation
ⓘ
concept in deformation quantization ⓘ concept in quantum mechanics ⓘ mathematical operation ⓘ |
| actsOn |
Wigner functions
NERFINISHED
ⓘ
functions on phase space ⓘ quasiprobability distributions ⓘ |
| appearsIn |
phase-space path integrals
ⓘ
quantum kinetic theory ⓘ quantum optics ⓘ quantum transport theory ⓘ |
| comparedTo | classical Liouville operator ⓘ |
| definedVia | commutator with respect to the Moyal star product ⓘ |
| describes | quantum corrections to classical dynamics ⓘ |
| encodes | quantum corrections as higher-order derivatives in phase space ⓘ |
| field |
deformation quantization
ⓘ
mathematical physics ⓘ phase-space quantum mechanics ⓘ quantum mechanics ⓘ |
| generalizes | Poisson bracket ⓘ |
| hasProperty |
antisymmetric
ⓘ
bilinear ⓘ noncommutative ⓘ nonlocal ⓘ satisfies Jacobi identity ⓘ |
| introducedBy | José Enrique Moyal NERFINISHED ⓘ |
| introducedIn | 1949 ⓘ |
| limit | Poisson bracket as Planck constant tends to zero ⓘ |
| mathematicallyFormulatedIn | phase-space coordinates position and momentum ⓘ |
| namedAfter | José Enrique Moyal NERFINISHED ⓘ |
| reducesTo | Poisson bracket in the classical limit ⓘ |
| relatedTo |
Moyal product
NERFINISHED
ⓘ
Wigner function NERFINISHED ⓘ Wigner–Weyl transform NERFINISHED ⓘ star product ⓘ |
| usedFor |
quantum Liouville equation
ⓘ
time evolution of quasiprobability distributions ⓘ |
| usedIn |
Wigner–Moyal formalism
NERFINISHED
ⓘ
phase-space formulation of quantum mechanics ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.