Aspects of relativistic quantum mechanics on phase space

  • S. Twareque Ali
1. Quantization Methods and Special Quantum Systems
Part of the Lecture Notes in Physics book series (LNP, volume 139)


Recent work on formulating relativistic quantum mechanics on stochastic phase spaces is described. Starting with a brief introduction to the mathematical theory of stochastic spaces, an account is given of non-relativistic quantum mechanics on stochastic phase space. The relativistic theory is introduced by constructing certain classes of representations of the Poincaré group on phase space, obtaining thereby both the classical and the quantum dynamics. Applications to the Dirac equation are discussed, and an alternative 2-component equation for a charged spin-1/2 particle, interacting with an external electromagnetic field is studied.


Hilbert Space Phase Space Quantum Mechanic Dirac Equation Unitary Irreducible Representation 
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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • S. Twareque Ali
    • 1
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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