Maxwell's equations, quantum physics and the quantum graviton

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10 Scopus citations


Quantum wave equations for massless particles and arbitrary spin are derived by factorizing the d'Alembertian operator. The procedure is extensively applied to the spin one photon equation which is related to Maxwell's equations via the proportionality of the photon wavefunction Ψ to the sum E + iB of the electric and magnetic fields. Thus Maxwell's equations can be considered as the first quantized one-photon equation. The photon wave equation is written in two forms, one with additional explicit subsidiary conditions and second with the subsidiary conditions implicitly included in the main equation. The second equation was obtained by factorizing the d'Alembertian with 4×4 matrix representation of "relativistic quaternions". Furthermore, scalar Lagrangian formalism, consistent with quantization requirements is developed using derived conserved current of probability and normalization condition for the wavefunction. Lessons learned from the derivation of the photon equation are used in the derivation of the spin two quantum equation, which we call the quantum graviton. Quantum wave equation with implicit subsidiary conditions, which factorizes the d'Alembertian with 8×8 matrix representation of relativistic quaternions, is derived. Scalar Lagrangian is formulated and conserved probability current and wavefunction normalization are found, both consistent with the definitions of quantum operators and their expectation values. We are showing that the derived equations are the first quantized equations of the photon and the graviton.

Original languageEnglish
Article number012010
JournalJournal of Physics: Conference Series
Issue number1
StatePublished - 1 Jan 2011
Event7th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields, IARD 2010 - Hualien, Taiwan, Province of China
Duration: 30 May 20101 Jun 2010


  • Maxwell's equations
  • one photon quantum equation
  • quantum graviton

ASJC Scopus subject areas

  • General Physics and Astronomy


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