Lectures on Description of particles with any spin and with internal symmetry[MatSciRep:62]

Abstract

The problem considered here is that of describing free particles and antiparticles of definite nonzero mass m, spin s = 0, 1/2, 1, 3/2 and with internal symmetry. The particle is described by a wave function, the basis of representation of the Lorentz group. One value of the description is that it permits all properties of the free particle - discussed in a straight forward way, in parallel to the well-known discussions in Dirac Theory. Another usefulness of the description is that it gives an easy way to build up interactions. To make phenomenological interactions with form factors, one can simply combine the wave functions to make scalars. The relationship between all the formulations for spin 1 and for spin 3/2 were discussed by many, and also quantization of the theory has been studied. This present review follows Nelson and Good's work. Some background material has been added in the earlier sections and some subjects are discussed more at length here. However the original paper by 'Nelson and Good' contains more details and especially treatment of SU3 self conjugate multiplets. It is proved that the self conjugate fields have causal commutation rules. These ideas have been extended to SU3 multiplets.