Thermodynamic properties of a neutral vector boson gas in a constant magnetic field

The thermodynamical properties of a neutral vector boson gas in a constant magnetic field are studied starting from the spectrum given by Proca formalism. Bose-Einstein condensation (BEC) and magnetization are obtained in the limit of low temperature. In this limit, the condensation is reached not only by decreasing the temperature or augmenting the density but also by increasing the magnetic field. The magnetization turns out to be a positive quantity that increases with the field; under certain conditions self-magnetization is possible. The anisotropy in the pressures due to the axial symmetry imposed to the system by the magnetic field is also discussed. Astrophysical implications are commented.

Figure 1

The phase diagram in the $T-b$ plane for different values of particle density. The black dashed lines are the critical curves that separates the region of $T$ and $b$ when there is condensate (light gray region) from the region in which there is not (dark gray region). Note that the critical line also depends on the particle density.

Figure 2

The specific heat as a function of the temperature for $N={10}^{32}{\text{cm}}^{-3}$ and several values of the magnetic field.

Figure 3

Magnetization as a function of magnetic field for several values of the particle density (left panel). We have also plotted the $B/4\pi$. The solutions of self-magnetization equation as a function of particle density (right panel).

Figure 4

The pressure as a function of the magnetic field for several values of temperature (left panel); the statistical and the vacuum contributions to the pressure are also plotted in dashed and dot-dashed lines. The perpendicular pressure of the self-magnetized gas as a function of the particle density for several values of temperature (right panel).