Quantization of the massive gravitino on FRW spacetimes

Schenkel, Alexander; F. Uhlemann, Christoph

Abstract

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.

Citation

Schenkel, A., & F. Uhlemann, C. (2012). Quantization of the massive gravitino on FRW spacetimes. Physical Review D - Particles, Fields, Gravitation and Cosmology, 85(2), Article 024011. https://doi.org/10.1103/PhysRevD.85.024011

• Journal Article Type: Article
• Acceptance Date: Sep 20, 2011
• Online Publication Date: Jan 11, 2012
• Publication Date: Jan 11, 2012
• Deposit Date: Aug 22, 2019
• Print ISSN: 1550-7998
• Electronic ISSN: 1550-2368
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 85
• Issue: 2
• Article Number: 024011
• DOI: https://doi.org/10.1103/PhysRevD.85.024011
• Keywords: High Energy Physics - Theory; General Relativity and Quantum Cosmology; High Energy Physics - Phenomenology
• Public URL: https://nottingham-repository.worktribe.com/output/2460582
• Publisher URL: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.85.024011