Relativistic Hamiltonian Formalism in Quantum Field Theory and Micro-Noncausality

An attempt is made to extend Heisenberg-Pauli's theory of quantized fields in a rela-tivistically invariant way. The transformation theory of Dirac is used as a basis for that purpose. It is assumed that a mass variable is canonically conjugate to an invariant-time variable, being a common time to all fields. Considering that the field functions in the usual quantum field theory are those expressed in terms of a mass representation, we transform the field functions into those in an invariant-time representation. It is shown that in the new representation a relativistic Hamiltonian formalism of quantum field theory can be obtained and the configuration space method in nonrelativistic case can be generalized. The new formalism is applied to the bound state problem. It is shown that, for the inter-actions between two particles in bound states, the condition of micro-noncausality plays an important role. As simple examples, the bound states of deuteron-like and hydrogen-like systems are discussed. For simplicity the new formalism is developed for charged sp,in zero fields, but the extension to other cases is obvious