Abstract
Ward-Takahashi relations for spin symmetry $\mathrm{SU}{(2)}_{\mathrm{S}}$ and pseudospin symmetry $\mathrm{SU}{(2)}_{\mathrm{C}}$ are derived for the simple Hubbard model in arbitrary dimensions. For this purpose we generally discuss local SO(4) symmetry in terms of Clifford algebra, and employ a gauge transformed form of the original Hubbard Hamiltonian, which makes the Ward-Takahashi relations much simpler. Derived Ward-Takahashi relations are rewritten as the relations between self-energy and vertex part to discuss spontaneously broken symmetry and Fermi liquid property of the system for zero temperature magnetism.
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