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.