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arXiv:0909.2429 · International Journal of Theoretical Physics

Quantum Wave Equation of Photon

Xiang-Yao Wu, Xiaojing Liu, Yiheng Wu, Qingcai Wang, Yan Wang, Li-Xin Chi

Published Nov 20, 2009• 12 citations
arXivHTMLPDF
DOI
10.1007/s10773-009-0192-x

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It is shown that a Dirac(-type) equation for a rank-two bi-spinor field ψph on Minkowski (configuration) spacetime furnishes a Lorentz-covariant quantum-mechanical wave equation in position-space representation for a single free photon. This equation does not encounter any of the roadblocks that have obstructed previous attempts (by various authors) to formulate a quantum-mechanical photon wave equation. In particular, it implies that the photon wave function ψph yields conserved non-negative Born-rule-type quantum probabilities and that its probability current density four-vector transforms properly under Lorentz transformations. Moreover, the eigenvalues of the pertinent photon Dirac Hamiltonian and the vector eigenvalues of the photon momentum operator yield the familiar Einstein relations E = ℏω and p = ℏk, respectively. Furthermore, these spin-1 wave modes are automatically transversal without the need of an additional constraint on the initial data. Some comments on other proposals to set up a photon wave equation are supplied as well.