Re: EM field of photon

Our photon wave function papers seem to have become an integral part
of the "EM field of photon thread" between Dec.11 2007 and Jan.7 2008.
This is great fun, and I am happy to respond now that you have pointed
this out to me. However, it is important not to loose the forest while
looking at the trees, and I think following the tread will just be
more trees. We wrote a series of papers on photon position operators
and wave functions.

1999, Phys. Rev. A 59, 954, brute force construction of a position
operator with commuting components and transverse eigenvectors,

1999, Phys. Rev. A 59, 3223, naïve wave function paper, but wave
function is A, and it is covariant

2001, arXiv:quant-ph/0101011, generalization of the 1999 position op
from momentum space spherical polar coordinates to include all
possible transverse basis using Euler angles. There is mathematically
analogous to the magnetic monopole in coordinate space, and we got
carried away with analysis of it, but I don't think this analogy is
very important physically. This is the paper that became the subject
of discussion in January. We called the position operator a matrix
because it involves the spin-1 operator. This was in an attempt to
avoid confusion, but it appears that it caused more confusion than it
avoided.

2004, arXiv:quant-ph/0408017. Here I think we got to the heart of the
physical interpretation, based on my new found understanding of the
angular momentum of optical beams after reading the literature on this
subject. We found that It is not possible to construct a transverse
localized state without introducing a vortex structure. Thus the
localized states are not spherically symmetric, and this is why our
position operator does not transform as a vector. Viewed from another
coordinate system, the axis of the vortex may be rotated, and the
extra term in the position operator just rotates this axis. I don't
think there is anything unphysical about this.

2007, arXiv:0711.0112. The eigenvectors of our photon position
operator form a basis of transverse and longitudinal localized states.
The qed state vector |psi> can be projected onto this basis, giving a
coordinate space photon wave function. It looks like <0|A|psi> where A
is a qed operator, eg the vector potential. It is not the usual
expectation value, <psi|A|psi>.

2007, arXiv:0705.3196. This is an earlier expanded version of the
above and quite an extensive discussion of the photon wave function
literature.

I hop to respond to the Jan.7 comments later.


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