Thermodynamic functions of a relativistic electron gas on a tube in a magnetic field

On the basis of the one-particle Dirac equation, an exact solution for the problem of the energy spectrum of a relativistic electron on the surface of a tube in a magnetic field is obtained. The spectra of a relativistic rotator and a relativistic electron in a two-dimensional electron gas are obtained in limiting cases. The density of electron states and the main thermodynamic functions of a relativistic electron gas on a tube in a magnetic field are calculated. These values experience Aharonov–Bohm oscillations and oscillations of the de Haas–van Alphen type with a change of the magnetic field and parameters of the problem. The asymptotics of thermodynamic functions at low- and high-temperatures are obtained. The results can be used in studies of nanotubes of a two-dimensional electron gas and in astrophysics.

CANONICAL QUANTIZATION AND MASS SPECTRUM OF RELATIVISTIC PARTICLE ANALOGUE OF RELATIVISTIC STRING WITH RIGIDITY

The generalized model of relativistic particle is studied. Its action contains the term for a free particle of mass m together with an additional term proportional to the curvature of its world trajectory. From the full set of Hamiltonian constraints, the mass shell condition is singled out and canonical quantization of the model is performed. The quantized system is shown to be equivalent to relativistic rotator with the mass spectrum coinciding with the spectrum of squared Majorana equation: [Formula: see text], where M is rotator’s mass, s is its spin and α−1 is a constant in additional term in action.