# Thermodynamical properties of a neutral vector boson gas in a constant magnetic field

## TL;DR

This paper investigates the thermodynamical behavior of a neutral vector boson gas under a constant magnetic field, revealing phase transitions, Bose-Einstein condensation, and magnetization effects in different dimensions, with astrophysical implications.

## Contribution

It provides a detailed analysis of BEC and magnetization phenomena in neutral vector boson gases using Proca formalism, highlighting effects of magnetic fields in various dimensions.

## Key findings

- In three dimensions, the gas undergoes a BEC phase transition with a critical temperature dependent on the magnetic field.
- In one dimension, a diffuse condensate appears similar to charged vector boson gases.
- Condensation can be achieved by decreasing temperature or increasing magnetic field, and self-magnetization is possible in both cases.

## Abstract

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, for the three and one dimensional cases, in the limit of low temperatures. In three dimensions the gas undergoes a phase transition to an usual BEC in which the critical temperature depends on the magnetic field. In one dimension a diffuse condensate appears as for the charged vector boson gas. In both cases, the condensation is reached not only by decreasing the temperature but also by increasing the magnetic field. In three and one dimensions self-magnetization is possible. The anisotropy in the pressures due to axial symmetry imposed to the system by the magnetic field is also discussed. The astrophysical implications are commented.