Sokolov demonstrated that relativistic quantum theories based on different forms of dynamics are related by S -matrix-preserving unitary transformations. The equivalence in field theories is more complicated because the definition of the field theory requires a redefinition of the ill-defined local operator products that appear in the dynamical generators. This is achieved through renormalization. At the perturbative level, the ultraviolet divergences of a canonical field theory are replaced by a mixture of ultraviolet and infrared ( P + = 0 ) divergences in light-front field theory. These have to be renormalized in a manner that recovers the full rotational covariance and maintains the S -matrix equivalence. The renormalization of light front field theories is discussed in Light-front computational methods#Renormalization group.