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Relativistic quantum mechanics over stochastic phase space

  • The Loyola Conference
  • Papers Presented at the Second New Orleans Conference of Quantum Theory and Gravitation, Loyola University, New Orleans, May, 1983
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Abstract

Stochastic quantum mechanics is a quantum theory in which the basic limitations of real-world measuring instruments, due to their intrinsically quantum nature, are taken into account. Among other things this leads to a new operational definition of space-time, called quantum space-time. Fundamental to this approach is the formulation of quantum mechanics over phase space rather than just over position or momentum space. A concept of extended particle is a natural outgrowth of this development. Gauge and internal symmetry have a natural place within the theory, and preliminary computations combining some old ideas due to Born with more recent ideas on symmetry breaking suggest that the theory could lead to a mass formula compatible with known data on the low-lying baryons.

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References

  • Ali, S. T., and Prugovečki, E. (1977).J. Math. Phys.,18, 219.

    Google Scholar 

  • Ali, S. T., and Prugovečki, E. (1983a). Extended harmonic analysis of phase space representations of the Galilei group, University of Toronto preprint.

  • Ali, S. T., and Prugovečki, E. (1983b). Harmonic analysis and systems of covariance for phase space representations of the Poincaré group, University of Toronto preprint.

  • Born, M. (1938).Proc. R. Soc. London Ser. A. 165, 291.

    Google Scholar 

  • Born, M. (1939).Proc. R. Soc. Edinburgh,59, 219.

    Google Scholar 

  • Born, M. (1949).Rev. Mod. Phys.,21, 463.

    Google Scholar 

  • Brooke, J. A., and Guz, W. (1982).Lett. Nuovo Cimento,35, 265.

    Google Scholar 

  • Brooke, J. A., and Guz, W. (1983a). Relativistic canonical commutation relations and the harmonic oscillator model of elementary particles,Nuovo Cimento A 78, 17.

    Google Scholar 

  • Brooke, J. A., and Guz, W. (1983b). The baryon mass spectrum and the reciprocity principle of Born.Nuovo Cimento A 78, 221.

    Google Scholar 

  • Brooke, J. A., and Prugovečki, E. (1982).Lett. Nuovo Cimento,33, 171.

    Google Scholar 

  • Brooke, J. A., and Prugovečki, E. (1984). Hadronic exciton states and propagators derived from reciprocity theory on quantum spacetime,Nuovo Cimento A 79, 237.

    Google Scholar 

  • Caianiello, E. (1980a).Lett. Nuovo Cimento,27, 89.

    Google Scholar 

  • Caianiello, E. (1980b).Nuovo Cimento,59B, 350.

    Google Scholar 

  • Landé, A. (1939).Phys. Rev.,56, 482, 486.

    Google Scholar 

  • Prugovečki, E. (1976).J. Math. Phys.,17, 517, 1673.

    Google Scholar 

  • Prugovečki, E. (1978a).Phys. Rev., D,18, 3655.

    Google Scholar 

  • Prugovečki, E. (1978b).J. Math. Phys.,19, 2260.

    Google Scholar 

  • Prugovečki, E. (1981a).Lett. Nuovo Cimento,32, 272.

    Google Scholar 

  • Prugovečki, E. (1981b).Lett. Nuvo Cimento,32, 481;33, 480.

    Google Scholar 

  • Prugovečki, E. (1982).Found. Phys. 12, 555.

    Google Scholar 

  • Prugovečki, E. (1984).Stochastic Quantum Mechanics and Quantum Spacetime. Reidel, Dordrecht.

    Google Scholar 

  • Takabayasi, T. (1979).Suppl. Prog. Theor. Phys.,67, 1.

    Google Scholar 

  • Yukawa, H. (1950a).Phys. Rev.,77, 219, 849,

    Google Scholar 

  • Yukawa, H. (1950b).Phys. Rev.,80, 1047.

    Google Scholar 

  • Yukawa, H. (1953).Phys. Rev.,91, 416.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, M5S 1A1, Toronto, Canada

    J. A. Brooke

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  1. J. A. Brooke
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Supported in part by NSERC Grant, No. A8403.

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Brooke, J.A. Relativistic quantum mechanics over stochastic phase space. Int J Theor Phys 23, 783–799 (1984). https://doi.org/10.1007/BF02214066

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  • DOI: https://doi.org/10.1007/BF02214066

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