2016/03/02 by Charles Schwartz
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #CPT symmetry #Connection (principal bundle) #Helicity #Lorentz covariance #Lorentz group #Lorentz transformation #Noncommutative and Quantum Gravity Theories #Quantum and Classical Electrodynamics #Quantum field theory #Spinor #Tachyon #Tachyon condensation #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1142/s0217751x1650041x
published as Int. J. Mod. Phys. A 31 (9) 1650041 (2016) · 17 pages
arxiv created 2016/03/02 · openalex publication_date 2016/03/17 · arxiv updated 2016/03/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We construct momentum space expansions for the wave functions that solve the Klein–Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between space–time points separated by a timelike interval. Calculating the conserved charge and four-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.