A model of CPT violation for neutrinos

Any local relativistic quantum field theory of Dirac–Weyl fermions conserves CPT. Here we examine whether a simple nonlocal field theory can violate CPT. We construct a new relativistic field theory of fermions, which we call “homeotic”, which is nonlocal but causal and Lorentz invariant. The free homeotic theory is in fact equivalent to free Dirac theory. We show that a homeotic theory with a suitable nonlocal four-fermion interaction is causal and as a result has a well-defined perturbative S-matrix. By coupling a right-handed homeotic fermion to a left-handed Dirac–Weyl fermion, we obtain a causal theory of CPT-violating neutrino oscillations.