Photon polarization and Wigner's little group

Abstract

To discuss one-photon polarization states we find an explicit form of the Wigner's little group element in the massless case for arbitrary Lorentz transformation. As is well known, when analyzing the transformation properties of the physical states, only the value of the phase factor is relevant. We show that this phase factor depends only on the direction of the momentum $\vec{k}/|\vec{k}|$ and does not depend on the frequency $k^0$. Finally, we use this observation to discuss the transformation properties of the linearly polarized photons and the corresponding reduced density matrix. We find that they transform properly under Lorentz group.

Version published in Phys. Rev. A, few typos corrected

References in corpus (7)

• Quantum Entanglement of Moving Bodies
• Quantum entropy and special relativity
• Einstein-Podolsky-Rosen-Bohm experiment with relativistic massive particles
• Relativistic Einstein-Podolsky-Rosen correlation and Bell's inequality
• Relativistic Doppler effect in quantum communication
• Einstein-Podolsky-Rosen Correlations of Spin Measurements in Two Moving Inertial Frames
• Wigner's little group and Berry's phase for massless particles

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