Baryon number violation and novel canonical anti-commutation relations

TL;DR

This paper investigates how baryon number violating terms modify the canonical anti-commutation relations of neutrons, revealing novel quantum behavior with implications for neutron-antineutron oscillations and Majorana fermions.

Contribution

It demonstrates that baryon number violation alters the canonical anti-commutation relations, introducing a new quantum behavior analyzed via a relativistic Bogoliubov transformation.

Findings

Modified anti-commutation relations due to baryon number violation

Degenerate Majorana fermions without neutron-antineutron oscillation

Application of relativistic Bogoliubov transformation

Abstract

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.