The 2d Gross-Neveu Model for Pseudovector Fermions and Tachyonic Mass Generation

Abstract

Recent observations in the OPERA experiment suggest that the neutrino could propagate with speed that is superluminal. Based on early theoretical work on tachyonic fermions we shall study a modification of the Gross-Neveu model in two dimensions. We shall see that the theory results to the dynamical generation of real and imaginary masses. These imaginary masses indicate the possibility that tachyonic solutions (or instabilities) could exist in the theory. The implications of a tachyonic neutrino coming from astrophysical sources are critically discussed. Moreover, we present a toy model that consists of an U(2,2) invariant Dirac Lagrangian. This theory can have tachyonic masses as solutions. A natural mass splitting between the solutions is a natural outcome of the formalism.

References added

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Cited by in corpus (7)

• Superluminal neutrinos and the tachyon's stability in the rotating Universe
• Superluminal neutrinos and domain walls
• Neutrino Shortcuts in Spacetime
• Superluminal Neutrinos and Monopoles
• Superluminal Neutrinos from OPERA Experiment and Weyl Equation
• Interacting tachyon Fermi gas
• Common origin of superluminal neutrinos and DAMA annual modulation