Local Tensor Fields and the Energy-Momentum Operator

Abstract

It is shown that for any local tensor field $f_{\mu \nu }\mathrm{}\left(x\right)\mathrm{}$ with certain natural properties, the space integral of $f_{0\nu }$ is proportional to the energy-momentum operator $P_{\nu }$. General conditions are established under which the agreement of a charge operator with the space integral of a local density on the one-particle subspaces implies their agreement on all of Hilbert space.