2008/04/29 by Marek J. Radzikowski, Radzikowski, Marek J.
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.0804.4534
23 pages; corrected and clarified exposition; added further relevant references; included paragraph on frame-dependent interpretation rule
openalex publication_date 2008/04/29 · arxiv created 2008/05/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.