Energy and Momentum Density in Field Theory

Abstract

It is shown that the energy density commutator condition in its simplest form is valid for interacting spin 0, ½, 1 field systems, but not for higher spin fields. The action principle is extended, for this purpose, to arbitrary coordinate frames. There is a discussion of four categories of fields and some explicit consideration of spin $\frac{3}{2}$ as the simplest example that gives additional terms in the energy density commutator. As the fundamental equation of relativistic quantum field theory, the commutator condition makes explicit the greater physical complexity of higher spin fields.