Parametrized field theory

A theory is presented in which a field depends not only on spacetime coordinates x(mu), but also on a Lorentz-invariant parameter tau. Such a theory is conceptually and technically simple and manifestly covariant at every step. The generator of evolution and the generator of spacetime translations and Lorentz transformations are obtained in a straightforward way. In the quantized theory the Heisenberg equation of motion is written in a covariant form and is equivalent to the field equation. The equal tau commutator between the field and its canonically conjugate momentum is just proportional to the spacetimes delta function. Finally comparison with the conventional field theory is done, and it is found that the expectation value of the momentum operator in the on shell states is th same.