Configuration Space Methods in Relativistic Quantum Field Theory. I

Abstract

Three notions are introduced as a help in discussing the notion of particle in relativistic quantum field theory: particle interpretation, simple particle interpretation, and relevant simple particle interpretation. The problem of finding all solutions of the Heisenberg-Dirac commutation rules and Jordan-Wigner anti-commutation rules for annihilation and creation operators is posed and its solution indicated on the basis of work by G\aa{}rding and Wightman. Observables of particle position, momentum, and spin are introduced in accordance with the work of previous authors and the corresponding particle densities are expressed in terms of fields. The results disagree with those of previous authors. The relativistic transformation properties of fields are deduced from the corresponding properties for states in the case of no interaction. The use of "Schr\"odinger-type" relativity transformations makes this discussion completely elementary and makes possible a treatment of time inversion no more complicated than for other relativity transformations. The Schr\"odinger-type charge conjugation transformation is also discussed.