Foundations of Physics

, Volume 8, Issue 7–8, pp 573–591 | Cite as

Quantum mechanics of space and time

  • H. S. Green


A formulation of relativistic quantum mechanics is presented independent of the theory of Hilbert space and also independent of the hypothesis of spacetime manifold. A hierarchy is established in the nondistributive lattice of physical ensembles, and it is shown that the projections relating different members of the hierarchy form a semigroup. It is shown how to develop a statistical theory based on the definition of a statistical operator. Involutions defined on the matrix representations of the semigroup are interpreted in terms ofCPT conjugations. The theory of particles of spin one-half and systems with higher spin is developed from first principles. Methods are also developed for defining energy, momentum, orbital angular momentum, and weighted spacetime coordinates without reference to a manifold.


Manifold Hilbert Space Angular Momentum Quantum Mechanic Statistical Theory 
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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • H. S. Green
    • 1
  1. 1.Department of Mathematical PhysicsUniversity of AdelaideAdelaide

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