Localizability of Tachyonic Particles and Neutrinoless Double Beta Decay

Abstract

The quantum field theory of superluminal (tachyonic) particles is plagued with a number of problems, which include the Lorentz non-invariance of the vacuum state, the ambiguous separation of the field operator into creation and annihilation operators under Lorentz transformations, and the necessity of a complex reinterpretation principle for quantum processes. Another unsolved question concerns the treatment of subluminal components of a tachyonic wave packets in the field-theoretical formalism, and the calculation of the time-ordered propagator. After a brief discussion on related problems, we conclude that rather painful choices have to be made in order to incorporate tachyonic spin-1/2 particles into field theory. We argue that the field theory needs to be formulated such as to allow for localizable tachyonic particles, even if that means that a slight unitarity violation is introduced into the S matrix, and we write down field operators with unrestricted momenta. We find that once these choices have been made, the propagator for the neutrino field can be given in a compact form, and the left-handedness of the neutrino as well as the right-handedness of the antineutrino follow naturally. Consequences for neutrinoless double beta decay and superluminal propagation of neutrinos are briefly discussed.

12 pages, 5 figures

References in corpus (3)

• Measurement of the neutrino velocity with the OPERA detector in the CNGS beam
• Measurement of neutrino velocity with the MINOS detectors and NuMI neutrino beam
• Structure, Time Propagation and Dissipative Terms for Resonances

Cited by in corpus (26)

• Neutrinoless double beta decay and neutrino physics
• Tachyonic neutrinos and the neutrino masses
• From Generalized Dirac Equations to a Candidate for Dark Energy
• Generalized Householder Transformations for the Complex Symmetric Eigenvalue Problem
• Pseudo-Hermitian Quantum Dynamics of Tachyonic Spin-1/2 Particles
• Weighing the Neutrino
• Six observations consistent with the electron neutrino being a tachyon with mass: $m_{{\nu }_e}^2=-0.11\pm 0.016e{V}^2$
• Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory
• Ultrarelativistic Decoupling Transformation for Generalized Dirac Equations
• Gravitational Effects in g Factor Measurements and High-Precision Spectroscopy: Limits of Einstein's Equivalence Principle
• Calculation of the Decay Rate of Tachyonic Neutrinos against Charged-Lepton-Pair and Neutrino-Pair Cerenkov Radiation
• Quantum Field Theory of Space-like Neutrino
• Lepton-pair Cerenkov radiation emitted by tachyonic neutrinos: Lorentz-covariant approach and IceCube data
• Neutrino Helicity Reversal and Fundamental Symmetries
• Dispersion of Ultra-Relativistic Tardyonic and Tachyonic Wave Packets on Cosmic Scales
• Lorentz Breaking and SU(2)_L x U(1)_Y Gauge Invariance for Neutrino Decays
• Dirac Hamiltonian with Imaginary Mass and Induced Helicity-Dependence by Indefinite Metric
• Production of Tachyonic Neutrino in Matter
• Gravitational Correction to Vacuum Polarization
• Localized Propagating Tachyons in Extended Relativity Theories
• 3 neutrino mass experiments fit a strange 3 + 3 model, but will KATRIN reveal the model's unique 3-part signature?
• The Lorentz factor in a reverse coordinate system
• Equivalence Principle for Antiparticles and its Limitations
• Interacting tachyon Fermi gas
• Neutrino Pair Cerenkov Radiation for Tachyonic Neutrinos
• Dynamics of Neutrino Wave Packet in the Tachyon-like Dirac Equation