  In this article, we calculate the $S$-matrix elements for the process $e^{+}
e^{-}\rightarrow t \bar{t}$ mediated by SM photon, $Z$ boson and an additional
$Z^{'}$ boson indicating the contribution from new physics. We calculate the
amplitude square using two component spinor formalism and four component spinor
formalism and show the equivalence of the results using the two formalisms. We
also establish the relations between the couplings of $Z^{'}$ boson to fermions
in the two component spinor formalism and four component spinor formalism.
