On nonlocal, causal quantum field theory, applied to tachyonic neutrinos

Presented is a framework for viewing nonlocal behaviour in the context of quantum field theory, while maintaining a consistent semblance of causality. The framework is comprised of a model for a Klein-Gordon quantum field theory of tachyons on Minkowski spacetime, without exponentially growing modes, and yet with a sensible notion of causality. (The latter may be expressed as a ``no antitelephones'' or ``chronology protection'' property.) A criterion for the two-point function of the model, known as the ``microlocal spectral condition'', is found to be satisfied, suggesting a straightforward inclusion of the free QFT within a renormalizable interacting theory involving other particles (regular or tachyonic). Parity breaking is satisfied for the Dirac version at the free QFT level, suggesting an electroweak interaction involving only V coupling, assuming the tachyonic neutrino hypothesis of Chodos, Hauser and Kostelecky. Lorentz symmetry is necessarily spontaneously broken, requiring the notion of a ``tachyon'' frame, first developed by Ciborowski and Rembielinski. Such a ``tachyon frame'', viewed as respecting the principles of relativity, may be of use in describing other candidate nonlocal phenomena, e.g., as seen in quantum entanglement experiments.