Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED

E17385

result in quantum electrodynamics theoretical physics result

Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED is a landmark theoretical result that rigorously demonstrated the mathematical consistency and mutual compatibility of different approaches to quantum electrodynamics.

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All labels observed (4)

Label	Occurrences
Dyson series expansion for the S-matrix	1
Dyson’s formulation of quantum electrodynamics	1
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED canonical	1
Relativistic formulation of quantum field theory	1

Statements (44)

Predicate	Object
instanceOf	result in quantum electrodynamics ⓘ theoretical physics result ⓘ
author	Freeman Dyson ⓘ
clarifies	relationship between Feynman diagrams and operator methods ⓘ status of Feynman diagrams as a systematic expansion ⓘ
concerns	covariant formulation of QED ⓘ operator formalism in QED ⓘ path-integral inspired Feynman diagram method ⓘ
context	postwar development of relativistic quantum field theory ⓘ resolution of infinities in quantum electrodynamics ⓘ
demonstratesEquivalenceOf	Feynman path integral ⓘ surface form: Feynman formulation of QED Tomonaga–Schwinger equation ⓘ surface form: Schwinger–Tomonaga formulation of QED Tomonaga–Schwinger equation ⓘ surface form: Tomonaga–Schwinger formalism
establishes	mathematical consistency between different QED formulations ⓘ mutual compatibility of Feynman and Schwinger–Tomonaga approaches ⓘ
field	quantum electrodynamics ⓘ quantum field theory ⓘ
historicalPeriod	late 1940s ⓘ
influenced	pedagogical treatments of perturbative QED ⓘ subsequent work on axiomatic quantum field theory ⓘ
involves	comparison of S-matrix elements ⓘ covariant perturbation expansion ⓘ expansion of the S-matrix in powers of the coupling constant ⓘ time-ordered exponential of the interaction Hamiltonian ⓘ
relatedToPerson	Julian Schwinger ⓘ Richard Feynman ⓘ Sin-Itiro Tomonaga ⓘ
relatedWork	S-matrix ⓘ surface form: Dyson’s papers on the S-matrix in quantum electrodynamics
relatesTo	Feynman diagrams ⓘ Tomonaga–Schwinger equation ⓘ covariant commutation relations ⓘ
shows	Feynman rules reproduce Tomonaga–Schwinger operator results order by order ⓘ Lorentz invariance of the perturbation expansion can be maintained ⓘ diagrammatic expansion corresponds to time-ordered products of interaction terms ⓘ
significance	contributed to acceptance of Feynman diagram technique ⓘ helped unify competing formulations of QED ⓘ landmark result in the development of renormalized QED ⓘ provided rigorous foundation for perturbative QED calculations ⓘ
supports	view that different QED formalisms are representations of the same underlying theory ⓘ
usesConcept	Dyson series ⓘ S-matrix ⓘ interaction picture ⓘ perturbation theory in QED ⓘ time-ordered products ⓘ

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Freeman Dyson → notableWork → Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED ⓘ

Sin-Itiro Tomonaga → notableWork → Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED ⓘ

this entity surface form: Relativistic formulation of quantum field theory

Dyson → notableWork → Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED ⓘ

subject surface form: Freeman Dyson

this entity surface form: Dyson’s formulation of quantum electrodynamics

Gell-Mann–Low theorem → implies → Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED ⓘ

this entity surface form: Dyson series expansion for the S-matrix