Note on Spin-Wave Operators

Abstract

If, together with the spin lowering operator S−, which creates a spin deviation, we consider the operator Ŝ+ = Q−s (S+Sz)−1 S+, where Q−s excludes the Sz = − S state, we can show that the number of spin deviations S − Sz = S−Ŝ+, and the operators obey the commutation relations [Ŝ+, S−] = 1 − (2S+1) P−s, where P−s is the projection operator for the − S state. The Heisenberg spin Hamiltonian written in terms of these operators assumes the Dyson form. We compare the Ŝ+, S− operators with ideal spin wave operators, and also use them to obtain the random-phase approximation results in a simple and revealing form.