Second-Quantization Process for Particles with Any Spin and with Internal Symmetry

Abstract

In this paper, the second-quantized theory of free particles and antiparticles, with any spin and with internal $\mathrm{SU}\left(2\right)\mathrm{}$ or $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry, is developed. All spins and both statistics are treated in a uniform way in terms of well-defined complete sets of functions that are orthonormal with respect to a Lorentz-invariant positive-definite inner product. Explicit formulas for field operators of energy, momentum, etc., are given, including three-vector, four-vector, and tensor operators for polarization. It is shown that causal space densities of physical quantities exist when the correct spin-statistics connection is used. The field operators for systems self-conjugate under $C$, $G$, and $\mathrm{GP}$ are treated and self-conjugate multiplets of $\mathrm{SU}\left(3\right)\mathrm{}$ are set up.