Bargmann-Wigner equations in five-dimensional space

The linearisation of the Schrodinger equation leads to a description of odd-even nuclei with spin 3/2 in the ground state. In order to generalise this description to nuclei with arbitrary spins in their ground states, we construct the Bargmann-Wigner equations (BWEs) for the [1, 1]SO(5)-representation, which can be applied to odd-odd nuclei with spins 1 and 3, and for the [3/2, 3/2]SO(5)-representation which can describe odd-even nuclei having ground-state spins of 3/2, 5/2 and 9/2. We also present the nonrelativistic limit of the BWE for [1, 1]SO(5)-representation in the case of a particle moving in an electromagnetic field with minimal coupling.