Inconsistencies of massive charged gravitating higher spins. (English) Zbl 0995.83023
Summary: We examine the causality and degree-of-freedom (DoF) problems encountered by charged, gravitating, massive higher spin fields. For spin \(s=3/2\), making the metric dynamical, yields improved causality bounds. These involve only the mass, the product \(eM_P\) of the charge and Planck mass and the cosmological constant \(\Lambda\). The bounds are themselves related to a gauge invariance of the timelike component of the field equation at the onset of acausality. While propagation is causal in arbitrary E/M backgrounds, the allowed mass ranges of parameters are of Planck order. Generically, interacting spins \(s>3/2\) are subject to DoF violations as well as to acausality; the former must be overcome before analysis of the latter can even begin. Here we review both difficulties for charged \(s=2\) and show that while a g-factor of 1/2 solves the DoF problem, acausality persists for any \(g\). Separately we establish that no \(s=2\) theory - DoF preserving or otherwise - can be tree unitary.
MSC:
| 83C45 | Quantization of the gravitational field |
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