TY - JOUR

T1 - Quantization of the massive gravitino on FRW spacetimes

AU - Schenkel, Alexander

AU - Uhlemann, Christoph F.

N1 - 6 pages, 1 figure; published in PRD

PY - 2011/9/13

Y1 - 2011/9/13

N2 - 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.

AB - 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.

KW - hep-th

KW - gr-qc

KW - hep-ph

U2 - 10.1103/PhysRevD.85.024011

DO - 10.1103/PhysRevD.85.024011

M3 - Article

JO - Physical Review D. Particles, Fields, Gravitation, and Cosmology

JF - Physical Review D. Particles, Fields, Gravitation, and Cosmology

SN - 1550-7998

ER -