Field theory and symmetry rearrangement have provided a rather fertile ground to understand numerous phenomenon in particle physics and condensed matter physics at a deeper level. Such ideas have not found much use in nuclear systems. We explore the role of symmetry rearrangement or symmetry breaking in nuclei by considering the SU(4) spin-isospin s Y mmetry group. The low energy excitations such as isobaric analog states and Gamow-Teller states are a natural consequence as Nambu-Goldstone bosons. We obtain exact relations and establish inter-relationship between several quantities. It is quite likely that the dominant collective modes may be attributed to symmetry rearrangement.