Propagation and Quantization of Rarita-Schwinger Waves in an External Electromagnetic Potential

Quantized gauged massless Rarita-Schwinger fields

“…Another way of seeing this, noted by both Velo and Zwanziger [4] and Allcock and Hall [5], is that because 3 i=1 σ i σ i = 3, the expression W ij = δ ij − 1 2 σ i σ j is not a projector. But when one component of σ, say σ 3 , is replaced by 0, so that one has…”

“…Up to this point, we have not specialized L so as to make it easy to ascertain what the formulas become when gauge fixing is omitted (as in [3] and [4]). When L = 0, the matrix N degenerates to its upper left element A.…”

“…Here we turn to a detailed examination of quantization of a gauged massless Rarita-Schwinger field. Our main aim is to show that a consistent quantization is possible in gauge covariant radiation gauge, avoiding the problem of non-positivity of the canonical anticommutator first noted by Johnson and Sudarshan [3] and later rederived by Velo and Zwanziger [4]. Other objections to gauging a massless Rarita-Schwinger field -the issue of superluminal signaling, and various "on-shell no-go"theorems -have already been taken up in (I).…”

“…4 we give an alternative approach to proving positivity of the anticommutator in covariant radiation gauge, based on writing a Lagrangian for the equation of motion for Ψ in which Ψ 0 has already been eliminated by use of the secondary constraint. In Sec.…”

Quark transverse charge densities in the from lattice QCD

“…[26], this is the most general Lagrangian of this type that gives the right number of spin degrees of freedom for a spin-3/2 particle. This theory, however, would still lead to rather subtle pathologies such as non-causal wave propagation [27,28], at least if no other fields are present. Adding gravity in a supersymmetric way makes the theory fully consistent from this viewpoint, but also constrains the non-minimal couplings as follows:…”