SO(5) structure of p-wave superconductivity for the spin-dipole interaction model

A closed SO(5) algebraic structure in the pure p-wave superconductivity is found. It can help to diagonalize the the mean-field form of the Hamiltonian by making use of the Bogoliubov rotation instead of the Balian-Werthamer approach. We point out that the eigenstate is nothing but an SO(5)-coherent state with fermionic realization. By applying the approach to the Hamiltonian with Leggett dipole interaction the consistency between the diagonalization and gap equation is proved through the double-time Green function. The relationship between the s- and p-wave superconductivities turns out to be realized through Yangian algebra, a new type of infinite-dimensional algebra.