Non-Commutative Geometry and Measurements of Polarized Two Photon Coincidence Counts
S. Sivasubramanian, G. Castellani, N. Fabiano, A. Widom, J. Swain, Y. N. Srivastava, G. Vitiello
Abstract
Employing Maxwell's equations as the field theory of the photon, quantum mechanical operators for spin, chirality, helicity, velocity, momentum, energy and position are derived. The photon ``Zitterbewegung'' along helical paths is explored. The resulting non-commutative geometry of photon position and the quantum version of the Pythagorean theorem is discussed. The distance between two photons in a polarized beam of given helicity is shown to have a discrete spectrum. Such a spectrum should become manifest in measurements of two photon coincidence counts. The proposed experiment is briefly described.
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