Advertisement

Foundations of Physics

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

Quantum mechanics of space and time

  • H. S. Green
Article

Abstract

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.

Keywords

Manifold Hilbert Space Angular Momentum Quantum Mechanic Statistical Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. von Neumann,Mathematical Foundations of Quantum Mechanics (Princeton Univ. Press, Princeton, N.J., 1955).Google Scholar
  2. 2.
    I. M. Gel'fand,Generalized Functions, Vols. 2 and 4 (Academic Press, New York, 1968 and 1964).Google Scholar
  3. 3.
    G. Birkhoff and J. von Neumann,Ann. Math. 37, 823 (1936).Google Scholar
  4. 4.
    C. A. Hooker, ed.,Logico-algebraic Approach to Quantum Mechanics (D. Reidel, Dordrecht, Holland, 1975).Google Scholar
  5. 5.
    P. Suppes, ed.,Logic and Probability in Quantum Mechanics (D. Reidel, Dordrecht, Holland, 1976).Google Scholar
  6. 6.
    C. F. von Weizsäcker,Z. Naturforsch. 42, 521, 545 (1955);13A, 245, 705 (1958).Google Scholar
  7. 7.
    J. M. Blatt and C. A. Hurst,J. Aust. Math. Soc. 6, 221 (1966).Google Scholar
  8. 8.
    G. Birkhoff,Lattice Theory, 3rd ed. (AMS Colloquium Pubs. 25, 1967).Google Scholar
  9. 9.
    F. J. Murray and J. von Neumann,Ann. Math. 37, 116 (1936).Google Scholar
  10. 10.
    A. H. Clifford and G. B. Preston,Algebraic Theory of Semigroups (AMS Mathematical Surveys 7, 1961).Google Scholar
  11. 11.
    W. D. Munn,Q. J. Math. (Oxford) (2 11, 295 (1960).Google Scholar
  12. 12.
    L. de Broglie,Théorie Générale des Particules à Spin (Gauthier-Villars, Paris, 1943).Google Scholar
  13. 13.
    M. Fierz and W. Pauli,Proc. Roy. Soc. Lond. A173, 211 (1939); see also W. Rarita and J. Schwinger,Phys. Rev. 60, 61 (1941).Google Scholar
  14. 14.
    J. K. Lubanski,Physica 9, 310, 325 (1942).Google Scholar
  15. 15.
    H. J. Bhabha,Rev. Mod. Phys. 17, 200 (1945);Phil. Mag. 43, 33 (1952).Google Scholar
  16. 16.
    M. Gell-Mann,Phys. Rev. Lett. 8, 214 (1964);Aust. J. Phys. 29, 473 (1976); H. S. Green,Aust. J. Phys. 29, 483 (1976).Google Scholar
  17. 17.
    H. S. Green,Prog. Theor. Phys. 47, 1400 (1972).Google Scholar
  18. 18.
    Harish-Chandra,Phys. Rev. 71, 1933 (1947).Google Scholar
  19. 19.
    H. S. Green and A. J. Bracken,J. Math. Phys. 12, 2099 (1971); H. S. Green,J. Math. Phys. 12, 2106 (1971).Google Scholar
  20. 20.
    H. S. Green,Aust. J. Phys. 30, 1 (1977).Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

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

Personalised recommendations