Wigner function for charged particles with spin 0 in non-commutative space

Abstract

Wigner functions are quasi-probability distribution functions in phase space and play a crucial role in quantum optics, quantum information, and nuclear physics. In this paper,we first introduced the construction of the ${\star }_{\theta }$-product in non-commutative space and its relationship with the Wigner function. Then, we derived the eigenvalue equation of the Wigner function in non-commutative space using ${\star }_{\theta }$-product. Finally, we briefly discussed the role of $\theta$ in the observation of non-commutative effects in phase space within an electromagnetic field.