LSZ reduction formula
E59632
The LSZ reduction formula is a key result in quantum field theory that relates time-ordered correlation functions of fields to observable scattering amplitudes in the S-matrix.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
quantum field theory formula
→
scattering theory formalism → |
| appliesTo |
gauge theories
→
relativistic quantum field theories → scalar quantum field theories → spinor quantum field theories → |
| assumes |
adiabatic switching of interactions
→
asymptotic completeness → existence of asymptotic in and out states → |
| connects |
operator formalism and observable scattering data
→
|
| distinguishes |
free asymptotic fields
→
interacting Heisenberg fields → |
| expresses |
S-matrix elements as residues of Green's functions at particle poles
→
|
| field |
quantum field theory
→
theoretical physics → |
| formalismType |
reduction formula
→
|
| hasPurpose |
compute scattering amplitudes from correlation functions
→
|
| historicalPeriod |
mid 20th century
→
|
| holdsFor |
in and out asymptotic fields
→
|
| implies |
equivalence between field-theoretic description and particle scattering description
→
|
| isFoundationFor |
modern S-matrix theory in quantum field theory
→
|
| isToolFor |
deriving Feynman rules for scattering amplitudes
→
perturbative calculations in quantum field theory → |
| mathematicalNature |
limit of Fourier-transformed time-ordered correlators at on-shell momenta
→
|
| namedAfter |
Harry Lehmann
→
Kurt Symanzik → Wolfgang Zimmermann NERFINISHED → |
| relatedTo |
Feynman propagator
→
Haag-Ruelle scattering theory → S-matrix → Wightman functions → renormalization → |
| relates |
Green's functions
→
S-matrix elements → n-point correlation functions → scattering amplitudes → time-ordered correlation functions → |
| requires |
knowledge of full interacting Green's functions
→
|
| usedIn |
electroweak theory
→
high-energy particle physics → quantum chromodynamics → quantum electrodynamics → |
| usesConcept |
Fourier transform
→
amputated Green's functions → on-shell limit → pole structure of propagators → time-ordered products → wave-function renormalization constant → |
Referenced by (2)
| Subject (surface form when different) | Predicate |
|---|---|
|
S-matrix
→
|
relatedConcept |
|
Gell-Mann–Low theorem
→
|
relatedTo |