Baryon number violation and novel canonical anti-commutation relations

The possible neutron-antineutron oscillation is described by an effective quadratic Lagrangian analogous to the BCS theory. It is shown that the conventional equal-time anti-commutation relations of the neutron variable $n(t,\vec{x})$ are modified by the baryon number violating terms. This is established by the Bjorken--Johnson--Low prescription and also by the canonical quantization combined with equations of motion. This novel canonical behavior can give rise to an important physical effect, which is illustrated by analyzing the Lagrangian that violates the baryon number but gives rise to the degenerate effective Majorana fermions and thus no neutron-antineutron oscillation. Technically, this model is neatly treated using a relativistic analogue of the Bogoliubov transformation.