Low’s theorem
E1015932
Low’s theorem is a result in quantum electrodynamics that constrains the behavior of scattering amplitudes involving the emission of low-energy (soft) photons.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Low’s theorem canonical | 1 |
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
result in quantum electrodynamics
ⓘ
theorem ⓘ |
| appliesTo |
both tree‑level and loop‑corrected amplitudes (for soft limit structure)
ⓘ
processes with external charged particles ⓘ scattering amplitudes ⓘ |
| assumes | photon energy much smaller than characteristic energy scale of the process ⓘ |
| characterizes |
leading terms in soft‑photon expansion of amplitudes
ⓘ
subleading terms in soft‑photon expansion of amplitudes ⓘ |
| clarifies | universal nature of soft‑photon emission in QED ⓘ |
| concerns |
low‑energy photon emission
ⓘ
soft photons ⓘ |
| describes | behavior of scattering amplitudes with soft photon emission ⓘ |
| ensures | universal factorization of soft‑photon emission ⓘ |
| field | quantum electrodynamics ⓘ |
| holdsToOrder |
leading order in soft‑photon energy
ⓘ
subleading order in soft‑photon energy ⓘ |
| implies | soft‑photon factors depend only on external charges and momenta ⓘ |
| imposes | constraints on infrared behavior of amplitudes ⓘ |
| influenced | later developments in soft‑theorem program in quantum field theory ⓘ |
| involves | expansion of amplitudes in powers of photon momentum ⓘ |
| isDerivedUsing |
Lorentz invariance
ⓘ
analytic properties of scattering amplitudes ⓘ gauge invariance ⓘ |
| isFormulatedIn | momentum space ⓘ |
| isReferencedIn |
literature on infrared problems in gauge theories
ⓘ
quantum field theory textbooks ⓘ |
| isRelatedTo |
Bloch–Nordsieck mechanism
NERFINISHED
ⓘ
Weinberg’s soft‑photon theorem NERFINISHED ⓘ infrared divergences in QED ⓘ soft‑graviton theorems (by analogy) ⓘ soft‑photon theorems NERFINISHED ⓘ |
| isValidIn | on‑shell scattering processes ⓘ |
| originalContext | radiative corrections in quantum electrodynamics ⓘ |
| relates | amplitudes with and without an additional soft photon ⓘ |
| requires |
conservation of electric charge
ⓘ
on‑shell external charged legs ⓘ |
| usedFor |
checking consistency of QED calculations involving soft photons
ⓘ
deriving universal soft‑photon factors in scattering cross sections ⓘ understanding cancellation of infrared divergences between real and virtual photons ⓘ |
| wasFormulatedBy | Francis E. Low NERFINISHED ⓘ |
| yearProposed | 1958 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.