Tetradics Formulation of the Two-Time Green’s Function Method and Its Application to the Heisenberg Ferromagnet

Abstract

It is shown that the “tetradic” interpretation of Kubo’s H^× operator is convenient in writing the equation of motion for two-time Green’s function. In the formulation, the tetradics are used to express an anti-commutator of an operator as well as the commutator. For the Green’s function defined in terms of a commutator, the resulting equation of motion is equivalent to the one recently derived by Shimizu. A new approximation scheme is proposed on the basis of the obtained expression. Its lowest approximation is applied to the Heisenberg ferromagnet. It is shown how the results of the decouplings due to Tyablikov and others are derived as special cases in the present approximation scheme.