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

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

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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,

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