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International Journal of Theoretical Physics

, Volume 22, Issue 12, pp 1105–1121 | Cite as

Finite-dimensional quantum mechanics of a particle. III. The Weylian quantum mechanics of confined quarks

  • R. Jagannathan
Article

Abstract

A finite-dimensional analog of Weyl's formulation of quantum kinematics of a physical system through irreducible Abelian groups of unitary ray rotations in system space offers many possibilities for the quantum mechanics of confined particles. This paper is devoted to the expansion of the recently developed framework of such Weylian finite-dimensional quantum mechanics which may provide a new way of thinking about the characteristics of quark physics.

Keywords

Field Theory Elementary Particle Quantum Field Theory Quantum Mechanic Abelian Group 
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.

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References

  1. Alonso, M., and Valk, H. (1973).Quantum Mechanics: Principles and Applications, Addison-Wesley, Reading, Massachusetts, Section 11.13.Google Scholar
  2. Barut, A. O., and Bracken, A. J. (1980). InProceedings of IX International Colloquium on Group Theoretical Methods in Physics, Mexico (1980), K. B. Wolf, ed., Lecture Notes in Physics, Vol. 135, Springer-Verlag, Heidelberg, p. 206.Google Scholar
  3. Blokhinstev, D. I. (1973).Space and Time in the Microworld, D. Reidel Pub. Co., Dordrecht, Holland.Google Scholar
  4. Cole, E. A. B. (1973).Nuovo Cimento,A18, 445.Google Scholar
  5. Dadic, I., and Pisk, K. (1979).International Journal of Theoretical Physics,18, 345.Google Scholar
  6. Dober, V., and Yankovsky, G. (eds.) (1968).Philosophical Problems of Elementary Particle Physics, (English Translation) Progress Publishers, Moscow.Google Scholar
  7. Ehrlich, R. (1978).Physical Review,D18, 320.Google Scholar
  8. Finkelstein, D., Frye, G., and Susskind, L. (1974).Physical Review,D9, 2231.Google Scholar
  9. Ginsburg, V. L. (1976).Key Problems of Physics and Astrophysics, Mir Publishers, Moscow, Section 2.12.Google Scholar
  10. Glashow, S. L. (1980),Reviews of Modern Physics,52, 539.Google Scholar
  11. Heisenberg, W. (1966).Introduction to the Unified Theory of Elementary Particles, John Wiley, New York.Google Scholar
  12. Jagannathan, R., and Ranganathan, N. R. (1974).Reports on Mathematical Physics,5, 131.Google Scholar
  13. Jagannathan, R., and Ranganathan, N. R. (1975).Reports on Mathematical Physics,7, 229.Google Scholar
  14. Jagannathan, R. (1978).Matscience Report,93, 41.Google Scholar
  15. Jagannathan, R., Santhanam, T. S., and Vasudevan, R. (1981).International Journal of Theoretical Physics,20, 755.Google Scholar
  16. Jagannathan, R., and Santhanam, T. S. (1982).International Journal of Theoretical Physics,21, 351.Google Scholar
  17. Kadyshevsky, V. G. (1978). Toward a more profound theory of electromagnetic interactions. Preprint, Fermilab-Pub-78/70-THY.Google Scholar
  18. Kadanoff, L. P. (1977).Reviews of Modern Physics,49, 267.Google Scholar
  19. Kogut, J. B. (1979).Reviews of Modern Physics,51, 659.Google Scholar
  20. Lorente, M. (1981). Discreteness and continuum in quantum mechanics, Preprint, Max Planck Institut, Starnberg, Federal Republic of Germany.Google Scholar
  21. Ramakrishnan, A. (1971). (ed),Proceedings of the Conference on Clifford Algebra, Its Generalizations and Applications, Matscience Report, Madras.Google Scholar
  22. Ramakrishnan, A. (1972).L-Matrix Theory or Grammar of Dirac Matrices, Tata-McGraw Hill, New Delhi.Google Scholar
  23. Ramakrishnan, A., and Jagannathan, R. (1976). InTopics in Numerical Analysis, Miller, J. H. (ed.), Academic Press, New York, p. 133.Google Scholar
  24. Recami, E. (1981). Elementary particles as microuniverses, Preprint, Instituto Nationale di Fisica Nucleare, Catania, Italy, AE-81/3.Google Scholar
  25. Saavedra, I., and Utreras, C. (1981).Physics Letters,B98, 74.Google Scholar
  26. Salam, A. (1980),Reviews of Modern Physics,52, 525.Google Scholar
  27. Santhanam, T. S., and Tekumalla, A. R. (1976).Foundations of Physics,6, 583.Google Scholar
  28. Santhanam, T. S. (1977a).Foundations of Physics,7, 121.Google Scholar
  29. Santhanam, T. S. (1977b). InUncertainty Principle and Foundations of Quantum Mechanics, Price, W. and Chissick, S. S. (eds.), John Wiley, New York, p. 227.Google Scholar
  30. Santhanam, T. S. (1978). InProceedings of the 1978 International Meeting on Frontiers of Physics, Phua, K. K., Chew, C. K., and Lim, Y. K. (eds.), The Singapore National Academy of Sciences, Singapore, p. 1167.Google Scholar
  31. Schwinger, J. (1960a),Proceedings of the National Academy of Sciences (U.S.A.),46, 570.Google Scholar
  32. Schwinger, J. (1960b).Proceedings of the National Academy of Sciences (U.S.A.),46, 1401.Google Scholar
  33. Stovicek, P., and Tolar, I. (1979). Quantum mechanics in a discrete space-time, Preprint, ICTP, Trieste, Italy, Ic/79/147.Google Scholar
  34. Tati, T. (1980). The theory of finite degrees of freedom, Preprint, Research Institute for Theoretical Physics, Hiroshima University, Hiroshima, Japan.Google Scholar
  35. 't Hooft, G. (1981).Physica Scripta,24, 841.Google Scholar
  36. Vyaltsev, A. N. (1965).Discrete Space-Time, Nauka, Moscow.Google Scholar
  37. Weinberg, S. (1980).Reviews of Modern Physics,52, 515.Google Scholar
  38. Weyl, H. (1932).Theory of Groups and Quantum Mechanics, E. P. Dutton, New York, (Dover, New York, 1950), Section 4.14.Google Scholar
  39. Zidell, V. S. (1981).Physical Review,D23, 1221.Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • R. Jagannathan
    • 1
  1. 1.Institute of Mathematical SciencesMatscienceMadrasIndia

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