Question: Show that for a four-dimensional cartesian space ((x, y, z, t)) the operators which is the algebra associated with the group (mathrm{SO}(4)). Show that this

Show that for a four-dimensional cartesian space \((x, y, z, t)\) the operators

M = z a a a y M = x - M3

which is the algebra associated with the group \(\mathrm{SO}(4)\). Show that this \(\mathrm{SO}(4)\) is locally isomorphic to \(\mathrm{SU}(2) \times \mathrm{SU}(2)\) by showing that the new operator set,

= y x z z a N = y - 1 a

- N3 = 2 - - t N = X a -

M = z a a a y M = x - M3 = y x z z a N = y - 1 a - N3 = 2 - - t N = X a - - obey the Lie algebra [Mi, M;] Eijk Mk [Mi, Nj] = ijk Nk [Ni, Nj] = Eijk Mk,

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