On the spin content of the classical massless Rarita-Schwinger system

Abstract

We analyze the Rarita-Schwinger massless theory in the Lagrangian and Hamiltonian approaches. At the Lagrangian level, the standard gamma-trace gauge fixing constraint leaves a 1/2 and a 3/2 propagating Poincaré group helicities. At the Hamiltonian level, the result depends on whether the Dirac conjecture is assumed or not. In the affirmative case, a secondary first class constraint is added to the total Hamiltonian and a corresponding gauge fixing condition must be imposed, completely removing the 1/2 sector. In the opposite case, the 1/2 field propagates and the Hamilton field equations match the Euler-Lagrange equations.

Massless Rarita-Schwinger equations: Half and three halves spin solution

“…The general statement that "the spin-1 2 mode of the gravitino is pure gauge" seems to be in contradiction with the fact that the matter ansatz applied to the massless RS model (1) gives rise to the Dirac Lagrangian (16) and that the unconventional supersymmetry models describe propagating spin- 1 2 degrees of freedom. This contradiction is resolved in [15], and here we provide further evidence of the fact that spin- 1 2 sector of the vector-spinor propagates.…”

“…Complementing [15], here we show that the conclusion that the spin-1 2 sector of the massless RS system propagates can also be reached by fixing the gauge in an alternative way, and using the covariant spin-block projectors introduced by Behrends and Fronsdal [21] (see also [1,22]). As we shall see, this result is also valid for supergravity [12,13] and one can write explicitly the spin- 1 2 content in basic supergravity, consisting of the Dirac action coupled to the background geometry.…”

“…In [15] the Hamiltonian analysis of the massless RS system was carried out, and it was shown that the Dirac algorithm produces two different outputs depending on whether the Dirac conjecture-that secondary first-class constraints are gauge symmetry generators-is assumed or not.…”

“…where the spin-3 2 part ρ µ is gamma-traceless by construction and κ is a pure spin-1 2 mode. An indication of the non-trivial role of the spin- 1 2 sector is that the projection of the vector-spinor to the component ψµ = γ µ κ , (15) in the Lagrangian functional (1) reproduces the Dirac term,…”

“…More generally, the projection (15), dubbed the matter ansatz, can be used to generate models of spin- 1 2 fermions coupled to gravity and gauge interactions starting from supersymmetry gauge connections, of the form…”