Problems and Progress in Covariant High Spin Description

Abstract

A universal description of particles with spins j ≥ 1, transforming in (j, 0) ⊕ (0, j), is developed by means of representation specific second order differential wave equations without auxiliary conditions and in covariant bases such as Lorentz tensors for bosons, Lorentz-tensors with Dirac spinor components for fermions, or, within the basis of the more fundamental Weyl-Van-der-Waerden sl(2, C) spinor-tensors. At the root of the method, which is free from the pathologies suffered by the traditional approaches, are projectors constructed from the Casimir invariants of the spin-Lorentz group, and the group of translations in the Minkowski space time.

On the choice of relativistic wave equation for the particle having spin s = 3/2

“…The main problem is an interaction with external fields. These difficulties of the Rarita-Schwinger equation were mentioned by many researchers, see, for example, [24][25][26][27][28][29][30][31][32][33][34][35].…”

“…It should be noted especially that the theoretical description of the elementary particles with spin 3/2 in the frameworks of field theory still deals with a number of fundamental problems (see, e.g., [24][25][26][27][28][29][30][31][32][33][34][35], as well as [13][14][15][16]). This is typical for all fields with higher spins that are larger than s = 1.…”

“…It is clear that the authors of publications [ [13][14][15][16][24][25][26][27][28][29][30][31][32][33][34][35][36][37] tried to improve the theory. We have the same goal.…”

Massless Rarita–Schwinger field from a divergenceless antisymmetric tensor-spinor of pure spin-3/2

“…where u ± M (p) is one of the Majorana spinors in (33)(34), while ǫ 1,±1 (p) are the boosted transverse polarization vectors from (54-55), i.e.…”

“…At the level of the states, these helicities are excluded by the subtle Ward identities. Alternatively, as explained in [33] chiral projectors based on the pseudo-scalar Casimir invariant, G, of the Lorentz algebra,…”