In quantum mechanics, each Pauli matrix is related to an angular momentum operator that corresponds to an observable describing the spin of a spin particle, in each of the three spatial directions. As an immediate consequence of the Cartan decomposition mentioned above, are the generators of a projective representation (spin representation) of the rotation group SO(3) acting on non-relativistic particles with spin . The states of the particles are represented as two-component spinors. In the same way, the Pauli matrices are related to the isospin operator.
In quantum mechanics, each Pauli matrix is related to an angular momentum operator that corresponds to an observable describing the spin of a spin particle, in each of the three spatial directions. As an immediate consequence of the Cartan decomposition mentioned above, are the generators of ,a projective representation (spin representation) of the rotation group SO(3) acting on n?on-relativistic part:icles with spin . The states of the particles are represented as two-component spinors. In the same way, the Pauli matrices are related to the isospin operator.