  Recently, there has been renewed interest in a crossing-symmetric dispersion
relation from the 1970s due to its implications for both regular quantum field
theory and conformal field theory. However, this dispersion relation introduces
nonlocal spurious singularities and requires additional locality constraints
for their removal, a process that presents considerable technical challenges.
In this Letter, we address this issue by deriving a new crossing-symmetric
dispersion relation that is free of spurious singularities, resulting in a
compact form of the contact terms in crossing-symmetric blocks. Our results
establish a solid foundation for the Polyakov bootstrap in conformal field
theories and the crossing-symmetry S-matrix bootstrap in quantum field
theories.
