Symmetry Rearrangement of Spin and Isospin Symmetries and the Collective Modes in Nuclear Matter

Abstract A consistent theory of the spin and isospin excitations in an infinite nuclear system is formulated based on the Ward–Takahashi (W–T) relations among various many point Green's functions, which are derived from the requirement of the rotational invariance in spin and isospin space, SU(4). Collective modes are found to be six Nambu–Goldstone bosons, called spin, isospin, and spin–isospin waves, which appear as a result of the symmetry rearrangement of the SU(4) symmetry. The W–T relations are used to determine correlations among collective modes and to obtain a consistent expression for the static susceptibility beyond the random phase approximation. A consistent picture of the isovector collective excitations and their relationship to numerous experimental results is established. A partially conserved isovector current, analogous to a partially conserved axial current, in the symmetry rearrangement of isospin symmetry is established. This helps to define non-pertubatively the finite energy shift due to the explicit symmetry breaking terms.