Charged vector bosons in a magnetic field at a finite temperature

Bose–Einstein condensation does not occur in a charged vector boson gas in the presence of a homogeneous external magnetic field, although a major portion of the bosons are in the ground state. Spontaneous magnetization occurs in a vector boson gas. The total birth probability of vector boson pairs in a vacuum under a strong magnetic field at a finite temperature can be determined. Expressions that can probably characterize the vacuum free energy and magnetic moment are found, and formulas for the density and magnetic moment of the vector boson pairs generated by a magnetic field at a finite temperature are derived.