Crossing Symmetric Dispersion Relations in QFTs

Understand

For 2-2 scattering in quantum field theories, the usual fixed $t$ dispersion relation exhibits only two-channel symmetry.

• This paper considers a crossing symmetric dispersion relation, reviving certain old ideas in the 1970s.
• Rather than the fixed $t$ dispersion relation, this needs a dispersion relation in a different variable $z$, which is related to the Mandelstam invariants $s,t,u$ via a parametric cubic relation making the crossing symmetry in the complex $z$ plane a geometric rotation.
• The resulting dispersion is manifestly three-channel crossing symmetric.