Peierls bracket
E136243
bracket operation
mathematical concept
structure in classical field theory
structure in quantum field theory
The Peierls bracket is a covariant generalization of the Poisson bracket used in quantum field theory and classical field theory to define commutation relations in a way that respects spacetime causality.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Peierls bracket canonical | 2 |
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
bracket operation
ⓘ
mathematical concept ⓘ structure in classical field theory ⓘ structure in quantum field theory ⓘ |
| actsOn |
functionals of fields
ⓘ
observables in classical field theory ⓘ |
| alternativeTo | canonical Hamiltonian formalism in non-covariant coordinates ⓘ |
| basedOn | action functional of a field theory ⓘ |
| clarifies | relation between classical causality and quantum commutators ⓘ |
| compatibleWith | relativistic invariance ⓘ |
| definedInTermsOf | difference between advanced and retarded effects of perturbations ⓘ |
| dependsOn | choice of action and boundary conditions ⓘ |
| ensures | microcausality in field theory formulations ⓘ |
| field |
classical field theory
ⓘ
covariant Hamiltonian formalism ⓘ mathematical physics ⓘ quantum field theory ⓘ theoretical physics ⓘ |
| formalismType | Lagrangian-based bracket construction ⓘ |
| historicalPublication | Rudolf Peierls' 1952 paper on commutation laws of relativistic field theories ⓘ |
| inspired | covariant phase space approaches to field theory ⓘ |
| namedAfter | Rudolf Peierls ⓘ |
| property |
antisymmetric bilinear operation
ⓘ
covariant with respect to spacetime transformations ⓘ reduces to the canonical Poisson bracket in suitable limits ⓘ respects spacetime causality ⓘ satisfies the Jacobi identity under appropriate conditions ⓘ |
| quantizationRole | provides a route from classical to quantum commutators ⓘ |
| relatedTo |
Green's functions
ⓘ
Poisson bracket ⓘ advanced Green's function ⓘ canonical commutation relations ⓘ covariant phase space ⓘ retarded Green's function ⓘ |
| usedFor |
constructing quantum commutators from classical field theory
ⓘ
defining commutation relations in field theory ⓘ formulating dynamics in a manifestly covariant way ⓘ generalizing the Poisson bracket in a covariant way ⓘ |
| usedIn |
algebraic quantum field theory
ⓘ
covariant canonical quantization ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Rudolf Peierls