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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 propertiesof two dimensional (2D) strongly interacting fermions and the results have beenapplied to 2D liquid $^3He$ as the only real fermion system. Our results showthat this variational method, known as lowest order constrained variationalmethod, can be used to relativistic 2D fermion systems with a good accuracy. Inthe case of 2D liquid $^3He$, Our calculations showed that at highertemperatures relativistic effects are more significant and quantum mechanicaleffects play a minor role. Also, we have found that in this system, asexpected, relativistic effects are not considerable at low temperatures.

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