1206.1668 (Chun-Fang Li)
Chun-Fang Li
A notion called correlation between the intrinsic degree of freedom and the extrinsic degree of freedom is introduced from the transversality condition. Any particular three-component wavefunction $\mathbf f$ that is restricted by the transversality condition is expressed in terms of a correlation operator $\Pi$ and a two-component wavefunction $\tilde f$. In this way, the correlation operator $\Pi$ plays the role of connecting two different kinds of representations. In the so-called Maxwell representation, the wavefunction $\mathbf f$ carries the correlation; the operator of physical quantity does not. In the so-called Jones representation, the wavefunction $\tilde f$ does not carry the correlation; the operator does. Not suffering from any restrictions, $\tilde f$ appears to be the wavefunction about the intrinsic degree of freedom. Furthermore, the fact that the transversality condition cannot completely determine $\Pi$ shows that the correlation operator possesses a kind of degree of freedom. So identified correlation degree of freedom may take the form of a unit vector $\mathbf I$ that is independent of the wavevector. From the point of view of the correlation, it indicates a multiple-to-one correspondence between the Maxwell representation and the Jones representation. When expressed in the Jones representation, all the physical quantities, including the spin and orbital angular momentum (OAM), show up to carry the correlation. The spin lies exactly in the wavevector direction, with the helicity being the component of newly defined polarization operator in the wavevector direction. The OAM about the origin splits into two parts, the OAM of the barycenter about the origin and the OAM about the barycenter. The former is dependent on the helicity as well as $\mathbf I$. The correlation degree of freedom $\mathbf I$ acts as a parameter to determine the helicity-dependent barycenter.
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http://arxiv.org/abs/1206.1668
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