Tomonaga–Schwinger equation
E71910
covariant generalization of the Schrödinger equation
equation in quantum field theory
relativistic wave equation
The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
Aliases (3)
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
covariant generalization of the Schrödinger equation
→
equation in quantum field theory → relativistic wave equation → |
| appliesTo |
interacting quantum field theories
→
relativistic quantum fields → |
| assumes |
locality of interactions
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microcausality of field operators → |
| basedOn |
covariance under Lorentz transformations
→
principle of relativity → |
| category |
relativistic quantum field equations
→
|
| clarifies |
role of time in relativistic quantum theory
→
|
| closelyRelatedTo |
Schrödinger functional equation in field theory
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|
| describes |
time evolution of quantum fields
→
unitary evolution between spacelike hypersurfaces → |
| developedBy |
Julian Schwinger
→
Sin-Itiro Tomonaga → |
| domain |
Minkowski spacetime
→
|
| ensures |
Lorentz-covariant description of quantum evolution
→
path-independence of evolution between hypersurfaces under suitable conditions → |
| expressedAs |
functional differential equation
→
|
| field |
quantum field theory
→
relativistic quantum mechanics → theoretical physics → |
| formulation |
covariant canonical formalism
→
|
| generalizationOf |
time-dependent Schrödinger equation
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|
| historicalPeriod |
mid-20th century
→
|
| influenced |
modern covariant formulations of quantum field theory
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|
| involves |
Hamiltonian density integrated over hypersurfaces
→
foliation of spacetime into spacelike hypersurfaces → |
| motivation |
to reconcile quantum dynamics with special relativity
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|
| namedAfter |
Julian Schwinger
→
Sin-Itiro Tomonaga → |
| relatedTo |
Dyson series
→
S-matrix → canonical quantization → covariant perturbation theory → interaction picture → path integral formulation of quantum field theory → |
| usedFor |
deriving covariant perturbation expansions
→
formulating interaction dynamics on arbitrary foliations of spacetime → |
| usesConcept |
Hamiltonian density
→
Heisenberg picture → functional derivative → spacelike hypersurface → state functional → |
Referenced by (5)
| Subject (surface form when different) | Predicate |
|---|---|
|
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
("Schwinger–Tomonaga formulation of QED")
→
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED ("Tomonaga–Schwinger formalism") → |
demonstratesEquivalenceOf |
|
Dirac equation
("Schrödinger equation")
→
|
extends |
|
Sin-Itiro Tomonaga
→
|
knownFor |
|
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
→
|
relatesTo |