Variational Calculations for Relativistic Two Dimensional Strongly Interacting Fermions: Application to 2D Liquid ${}^{3}He$

Instead of solving Dirac (or Klein-Gordon) equation for a many body system, in this paper a variational method has been used to investigate the properties of two dimensional (2D) strongly interacting fermions and the results have been applied to 2D liquid ${}^{3}He$ as the only real fermion system. Our results show that this variational method, known as lowest order constrained variational method, can be used to relativistic 2D fermion systems with a good accuracy. In the case of 2D liquid ${}^{3}He$, Our calculations showed that at higher temperatures relativistic effects are more significant and quantum mechanical effects play a minor role. Also, we have found that in this system, as expected, relativistic effects are not considerable at low temperatures.