  We develop crossing symmetric dispersion relations for describing 2-2
scattering of identical external particles carrying spin. This enables us to
import techniques from Geometric Function Theory and study two sided bounds on
low energy Wilson coefficients. We consider scattering of photons, gravitons in
weakly coupled effective field theories. We provide general expressions for the
locality/null constraints. Consideration of the positivity of the absorptive
part leads to an interesting connection with the recently conjectured weak low
spin dominance. We also construct the crossing symmetric amplitudes and
locality constraints for the massive neutral Majorana fermions and parity
violating photon and graviton theories. The techniques developed in this paper
will be useful for considering numerical S-matrix bootstrap in the future.
