CANONICAL QUANTIZATION OF NONLOCAL FIELD-EQUATIONS

We consistently quantize a class of relativistic nonlocal field equati ons characterized by a nonlocal kinetic term in the Lagrangian. We sol ve the classical nonlocal equations of motion for a scalar field and e valuate the on-shell Hamiltonian. The quantization is realized by impo sing Heisenberg's equation, which leads to the commutator algebra obey ed by the Fourier components of the field. We show that the field oper ator carries, in general, a reducible representation of the Poincare g roup. We also consider the Gupta-Bleuler quantization of a nonlocal ga uge theory and analyze the propagators and the physical modes of the g auge field.