Abstract
We develop a functional integral formulation for the double exchange model with an infinitely large Hund's coupling, in which the local quantum spins are described by the ${\mathrm{CP}}^{1}$ spinor field. This formulation directly connects the quantum approach with classical approximation. The spin wave dynamics and the magnetic phase transition are studied by using a mean field approximation. The Curie temperature ${T}_{c}$ obtained is comparable to the experimental values in the manganese oxides. An instability of the uniform electron states against charge fluctuations caused by many-body correlation effect is also reported.
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