Physics

Scattering amplitude

Invariant (physics)

Pure mathematics

Mathematics

Mathematical physics

Lorentz transformation

Scalar field

Matrix (chemical analysis)

Unitarity

Quartic function

Quantum field theory

S-matrix

Composite material

Amplitude

Scattering

Materials science

Geometry

Quantum electrodynamics

Theoretical physics

Crossing

Quantum mechanics

Lorentz covariance

Scalar (mathematics)

Journal of High Energy Physics

A bstract We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 3+1 dimensions due to crossing symmetry, analyticity and unitarity. We extremize cubic couplings, quartic couplings and scattering lengths relevant for the elastic scattering amplitude of two identical scalar particles. In the cases where our results can be compared with the older S-matrix literature they are in excellent agreement. We also extremize a cubic coupling in 2+1 dimensions which we can directly compare to a universal bound for a QFT in AdS. This paper generalizes our previous 1+1 dimensional results of [1] and [2].

The S-matrix bootstrap. Part III: higher dimensional amplitudes