Irreducible representations of the rotation group in terms of the axis and angle of rotation

A. J. Torruella

The irreducible representations of the three-dimensional rotation group are obtained directly from the irreducible representations of its infinitesimal generators (the spin matrices), parametrized in terms of the rotation angle and the direction of the rotation axis. Expressions are given for the rotation operator exp(iψn ⋅ S) in terms of two different bases of 2j+1 elements for spin j. The results are related to the spectral decomposition of the rotation operator and expressions obtained for spin projection operators along any spatial direction for arbitrary spin.

S.S. Sannikov

Kamal Joshi, B. S. Rajput

The expression for matrix elements corresponding to finite complex rotations have been derived in terms of the complex Euler angles of the complex rotations. Using this expression the values of matrix elements for special cases of eigenvalues of complex angular momentum operator have been computed.

Felix M. Lev

Michael J. W. Hall, Marcel Reginatto

Arthur A. Broyles

An exchange operator is defined in terms of rotation and displacement operators. This operator contains a rotation around the z axis that produces a factor (−1)2s in front of the wave function. By postulating that such a rotation must produce the same value for the wave function if the particles are identical, we obtain the usual connection between spin and statistics. Particle states lying in the irreducible representations of the three-dimensional rotation group are seen to allow only Fermi and Bose statistics.