Aharonov–Bohm oscillations in relativistic Fermi and Bose systems

Aharonov–Bohm oscillations (the reaction to the field of a solenoid) are studied for Fermi and Bose systems with a relativistic form of the spectrum. It is shown that in multiply connected spaces $R^d\times S^1$ the effective potential of the fermion models (for both ordinary and twisted fermions) oscillates when the magnetic field flux is varied. The contribution of the oscillations to the free energy of the system at a finite temperature is found. The Gross–Neveu model in linear (on a finite interval) and ring geometry is studied in detail. It is shown that the normal and twisted fermions lead to a different dependence of the order parameter on the length of the ring. In the case of linear geometry and in the framework of the mean field approximation there exists a minimal length at which a phase transition of the second kind to a state with restored symmetry occurs. A new (instanton) mechanism of Aharonov–Bohm oscillations is predicted for models of a real scalar field with periodic potential (of sine-Gordon type) when the interaction of the field with the electromagnetic potential is described by topological terms.