Stable, Renormalizable, Scalar Tachyonic Quantum Field Theory with Chronology Protection
Abstract
Description
We use microlocal arguments to suggest that Lorentz symmetry breaking must occur in a reasonably behaved tachyonic quantum field theory that permits renormalizability. In view of this, we present a scalar tachyonic quantum field model with manifestly broken Lorentz symmetry and without exponentially growing/decaying modes. A notion of causality, in which anti-telephones are excluded, and which is viewed as a form of chronology protection, is obeyed. The field theory is constructed in a preferred tachyon frame in terms of commuting creation/annihilation operators. We calculate some sample (renormalized) operators in this preferred frame, argue that the Hadamard condition is satisfied, and discuss the PCT and spin-statistics theorems for this model.
23 pages; corrected and clarified exposition; added further relevant references; included paragraph on frame-dependent interpretation rule
23 pages; corrected and clarified exposition; added further relevant references; included paragraph on frame-dependent interpretation rule