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Versione delle 11:45, 1 ago 2023

Versione attuale delle 11:57, 1 ago 2023

Riga 88:

'''propagator.'''

Andrew Strominger - Lectures on the Infrared Structure of Gravity and Gauge Theory, p. 35

Riga 100 ⟶ 98:

Weinberg’s soft graviton theorem<ref name=":0" /> is a universal formula relating any S-matrix element in any quantum theory including gravity to a second S-matrix element which differs only by the addition of a graviton whose four-momentum is taken to zero. Remarkably, the formula is blind to the spin or any other quantum numbers of the asymptotic particles involved in the S-matrix element.

https://dash.harvard.edu/bitstream/handle/1/29374083/1401.7026.pdf;jsessionid=6392FB47A36DFFDF342EC0BC22893C9E?sequence=1

''Consider an amplitude M involving some incoming and some outgoing particles. Now, consider the same amplitude with an additional soft-photon (''<math>\omega_{\text{photon}} \to 0</math>'') coupled to one of the particles. Call this amplitude M'. The two amplitudes are related by''

<math>{\cal M}' = {\cal M} \frac{\eta q p \cdot \epsilon}{p \cdot p_\gamma - i \eta \varepsilon}</math>

''where p is the momentum of the particle that the photon couples to,'' <math>\epsilon</math>'' is the polarization of the photon and'' <math>p_\gamma</math>'' is the momentum of the soft-photon.  ''<math>\eta = 1</math>''for outgoing particles and'' <math>\eta = -1</math>'' for incoming ones. Finally, q is the charge of the particle.''

the proportionality factor relating M and M' is independent of the type of particle that the photon couples to.

== Note ==