Ultralocal approach to quantum field theory: a survey of present results

Studies have been made of various ultralocal model theories which differ formally from their covariant analogous in that the epacial gradients are dropped from the Hamiltonian. In such models the field operator is rigorously determined as bilinear expression in terms of conventional creation and annihilation operators. All ultralocal interacting fields violate standard canonical (anti) commutation relations, and lead to nontrivial renormalized field operator products (other than conventional normal ordering). Only symmetry and general quantum principles are used in obtaining these results; absolutely no cutoffs or perturbation there are introduced.
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