Quantum field theory of particle oscillations: Neutron-antineutron conversion

We formulate the quantum field theory description of neutron-antineutron oscillations in the framework of canonical quantization, in analogy with the Bardeen–Cooper–Schrieffer theory and the Nambu–Jona-Lasinio model. The physical vacuum of the theory is a condensate of pairs of would-be neutrons and antineutrons in the absence of the baryon-number violating interaction. The quantization procedure defines uniquely the mixing of massive Bogoliubov quasiparticle states that represent the neutron. In spite of not being mass eigenstates, neutron and antineutron states are defined on the physical vacuum and the oscillation formulated in asymptotic states. The exchange of the baryonic number with the vacuum condensate engenders what may be observed as neutron-antineutron oscillation. The convergence between the present canonical approach and the Lagrangian/path integral approach to neutron oscillations is shown by the calculation of the anomalous (baryon-number violating) propagators. The quantization procedure proposed here can be extended to neutrino oscillations and, in general, to any particle oscillations.