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Hans de Vries
#1
Dec9-07, 03:25 PM
Sci Advisor
P: 1,135
The electromagnetic Chern Simons spin density

is only know since the nineteen seventies from advanced Quantum Field Theory
on the chiral anomalies. It is the correct form of the electromagnetic spin-
density of the vacuum. It can be expressed as a 4-vector as follows:

[tex] \mbox{Chern Simons Spin Density:}\qquad \vec{\cal S}\ =\
\textsf{D} \times \vec{A}\ \ +\ \ \textsf{H}\ \Phi\
,\qquad
{\cal S}^o \ =\ \frac{1}{c}(\textsf{D}\cdot\vec{A})\ \quad
[/tex]

Which are just the familiar electromagnetic potentials and fields.
It's still virtually unknown to the wider audience, hidden as it is in the
more advanced QFT texts in a less accessible form. Especially interesting
are the electromagnetic spin density fields of the electron and the photon.

For instance:

Linear polarized photons, originating from spin 1 transitions, don't carry net
spin, however, they still contain the information of the original spin sign within
the canceling, non zero, components of the EM spin density from electric and
magnetic vacuum polarization. Linear photons therefor come in two types
which might be physically distinguishable in entanglement experiments.

[tex]
\begin{array}{|l|c|c|c|c|}
\hline
&&&& \\
\mbox{polarization} &\ \ \mbox{orbit spin}\ \ &\ \mbox{EM spin}\ \vec{S}\ &\ \textsf{ D} \times \vec{A}\ & \ \ \ \textsf{ H}\ \Phi\ \ \\
&&&& \\ \hline &&&& \\
\mbox{Linear} & +\hbar & 0 & +\hbar & -\hbar \\
\mbox{Linear} & -\hbar & 0 & -\hbar & +\hbar \\
\mbox{Circular} & +\hbar & +\hbar & +\hbar & \ \ 0 \\
\mbox{Circular} & -\hbar & -\hbar & -\hbar & \ \ 0 \\
&&&& \\ \hline
\end{array}
[/tex]

The current experimental status suggests that we have to either, give up
locality and/or reality, or show that Malus law can be violated in polarizing
beam splitters. The two types of linear polarized photons might open the
door to the latter possibility.

The derivations (which I had to do myself since somehow one can't find
these anywhere) and many details can be found in my paper, here:

The electro magnetic Chern Simons spin density


Regards, Hans
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