Quantization of the massive gravitino on FRW spacetimes

Alexander Schenkel, Christoph F. Uhlemann
September 14, 2011
In this article we study the quantization and causal properties of a massive spin 3/2 Rarita-Schwinger field on spatially flat Friedmann-Robertson-Walker (FRW) spacetimes. We construct Zuckerman's universal conserved current and prove that it leads to a positive definite inner product on solutions of the field equation. Based on this inner product, we quantize the Rarita-Schwinger field in terms of a CAR-algebra. The transversal and longitudinal parts constituting the independent on-shell degrees of freedom decouple. We find a Dirac-type equation for the transversal polarizations, ensuring a causal propagation. The equation of motion for the longitudinal part is also of Dirac-type, but with respect to an `effective metric'. We obtain that for all four-dimensional FRW solutions with a matter equation of state p = w rho and w in (-1,1] the light cones of the effective metric are more narrow than the standard cones, which are recovered for the de Sitter case w=-1. In particular, this shows that the propagation of the longitudinal part, although non-standard for w different from -1, is completely causal in cosmological constant, dust and radiation dominated universes.
open access link Phys. Rev. D 85, 024011 (2012)
@article{Schenkel:2011nv, author = "Schenkel, Alexander and Uhlemann, Christoph F.", title = "{Quantization of the massive gravitino on FRW spacetimes}", journal = "Phys. Rev.", volume = "D85", year = "2012", pages = "024011", doi = "10.1103/PhysRevD.85.024011", eprint = "1109.2951", archivePrefix = "arXiv", primaryClass = "hep-th", SLACcitation = "%%CITATION = ARXIV:1109.2951;%%" }

Keywords: 
Rarita-Schwinger field, gravitino, QFT on curved spacetimes