Soft graviton theorem

In physics, the soft graviton theorem, first formulated by Steven Weinberg in 1965,^[1] allows calculation of the S-matrix, used in calculating the outcome of collisions between particles, when low-energy (soft) gravitons come into play.

Specifically, if in a collision between n incoming particles from which m outgoing particles arise, the outcome of the collision depends on a certain S matrix, by adding one or more gravitons to the n + m particles, the resulting S matrix (let it be S') differs from the initial S only by a factor that does not depend in any way, except for the momentum, on the type of particles to which the gravitons couple.^[2]

The theorem also holds by putting photons in place of gravitons, thus obtaining a corresponding soft photon theorem.

The theorem is used in the context of attempts to formulate a theory of quantum gravity in the form of a perturbative quantum theory, that is, as an approximation of a possible, as yet unknown, exact theory of quantum gravity.^[3]

In 2014 Andrew Strominger and Freddy Cachazo expanded the soft graviton theorem, gauge invariant under translation, to the subleading term of the series, obtaining the gauge invariance under rotation (implying global angular momentum conservation) and connected this to the gravitational spin memory effect.^[4]