No-Go Theorem

Majorana and the infinite component wave equations

“…Of course there are problems very similar to the ones listed for the case of dynamical groups, but the real problem here (and also in the other case) is the presence of the space-like solutions. Before discussing further this point I want to stress that, immediately after the formulation of the program of saturating the current algebra, a No-Go theorem was formulated by Grodsky and Streater [38]. These authors made the following assumptions:…”

Some Field-Theoretical Aspects of Two Types of the Poincaré Group Representations

“…While the condition (23), unlike (21), obviously depends on the proper Lorentz group representation realized in the corresponding space, the commutation relations (25) and (22) for the four-vector operators in physically different spaces are identical to each other.…”

“…Besides that, the FSIIR-class field theory can have such "deceases" as the lack of CP T -invariance [23], the violation of conventional connection between spin and statistics [24], the local noncommutativity of fields [25]. In what follows, we restrict ourselves to fields of class ISFIR or class FSFIR only, whose representations S(g) are decomposable into an infinite or finite direct sum of finite-dimentional irreducible representations of the proper Lorentz group, and which theory does not suffer from "deceases" listed above and does not possess tachyonic states.…”

Generalized Majorana and Nambu Equations with Antiparticles and the Reflection Properties

“…State vectors are written as ijm)a, yielding rP,a)/jm)a =-(j+112)ijm>a· We adopt the mass spectrum M/a> =JCI (j+ 112) for the particles and -M/a> = -JC I (j + 1 I 2) for the antiparticles. Representing the equations (reaJM/a> -JC) ijm)a=O and (FP,alM/a> +") X ijm)a=O in the covariant form, we obtain and (r,<a>p"+") ijm,P)a=O, (2) where [jm,P)a,a=exp(~K) /jm)a,a and X(cosh ~-1), ~2~3 (cosh ~-1), 1+~3 2 (cosh ~ -1)). For a more general momentum, we have only to add space rotations besides.…”