Advertisement

Measurement Techniques

, Volume 61, Issue 8, pp 755–759 | Cite as

Using Fundamental Physical Constants to Determine the Properties of Quantum Particles

  • V. V. Khruschov
FUNDAMENTAL PROBLEMS IN METROLOGY
  • 8 Downloads

The general Lie algebra for quantum operators of coordinates, momentum, and angular momentum of a quantum particle is investigated. In the limiting case, it becomes a Lie algebra for operators of canonical quantum field theory. Relations between operators of space-time symmetries of a quantum particle are considered. Operators obey a generalized algebra that depends on three new fundamental constants with dimensions of mass M, length L, and action H. Using representations of this algebra, we form generalized quantum HLM-fields with which HLM quantum particles are associated. It is shown that to take into account specific properties of these particles, it is necessary to modify the procedure of quantum measurements.

Keywords

Lie algebra Poincaré symmetry quantum field generalized space-time symmetry fundamental physical constant procedure of quantum measurements 

References

  1. 1.
    F. Indurain, Quantum Chromodynamics, Mir, Moscow (1986).Google Scholar
  2. 2.
    H. S. Snyder, “Quantized space-time,” Phys. Rev., 71, 38–41 (1947).ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Yu. A. Gol’fand, “On the introduction of the ‘elementary length’ into the relativistic theory of elementary particles,” ZhETF, 37, 504–509 (1959).Google Scholar
  4. 4.
    V. G. Kadyshevskii, “On the theory of quantization of space-time,” ZhETF, 41, 1885–1894 (1961).MathSciNetGoogle Scholar
  5. 5.
    M. Born, “A suggestion for unifying quantum theory and relativity,” Proc. R. Soc. Lond., A165, 291–303 (1938).ADSCrossRefGoogle Scholar
  6. 6.
    M. Born, “Application of ‘reciprocity’ to nuclei,” Proc. R. Soc. Lond., A166, 552–557 (1938).ADSCrossRefGoogle Scholar
  7. 7.
    C. N. Yang, “On quantized space-time,” Phys. Rev., 72, 874–874 (1947).ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    A. N. Leznov, “Generalization of the theory of the quantized space-time of snyder,” Pisma v ZhETF, 6, 821–823 (1967).Google Scholar
  9. 9.
    A. N. Leznov and V. V. Khruschev, The Most General Form of the Commutation Relations of the Theory of Discrete Space-Time, Preprint IFVE 73–38, Serpukhov (1973), pp. 1–9.Google Scholar
  10. 10.
    V. V. Khruschov, “Measurement of supersmall space-time volumes and introduction of new fundamental constants,” Izmer. Tekhn., No. 11, 10–11 (1992).Google Scholar
  11. 11.
    V. V. Khruschov, “The generalized symmetry groups for quantum theories in Minkowski space,” Proc. XV Workshop on High Energy Physics and Field Theory, Protvino, 1992, IHEP, Protvino (1995), pp. 114–118.Google Scholar
  12. 12.
    R. V. Mendes, “Deformations, stable theories and fundamental constants,” J. Phys., A27, 8091–8104 (1994).ADSMathSciNetzbMATHGoogle Scholar
  13. 13.
    C. Chryssomalakos and E. Okon, “Linear form of 3-scale special relativity algebra and relevance of stability,” Int. J. Mod. Phys., D13, 1817–1822 (2004).ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    C. Chryssomalakos and E. Okon, “Generalized quantum relativistic kinematics: a stability point of view,” Int. J. Mod. Phys., D13, 2003–2034 (2004).ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    M. Toller, “Events in a noncommutative space-time,” Phys. Rev., D70, No. 024006, 1–13 (2004).MathSciNetGoogle Scholar
  16. 16.
    V. V. Khruschev, “Symmetries of fundamental interactions in quantum phase space,” Grav. Cosmol., 15, 323–326 (2009).ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    A. N. Leznov, “The wavelength of the modified spacetime manifold,” ArXiv, 1604.00672 [physics.gen-ph] (2016).Google Scholar
  18. 18.
    V. V. Khruschev and A. N. Leznov, “Relativistically invariant Lie algebras kinematic observables in quantum spacetime,” Grav. Cosmol., 9, 159–162 (2003).ADSzbMATHGoogle Scholar
  19. 19.
    V. V. Khruschev, “Modification of the measurement procedure of spatio-temporal observables with the introduction of additional fundamental constants,” Izmer. Tekhn., No. 7, 3–4 (1994).Google Scholar
  20. 20.
    V. V. Khruschev, “Relations between space-time values depending on additional fundamental constants,” Izmer. Tekhn., No. 12, 3–6 (1997).Google Scholar
  21. 21.
    V. V. Khruschev, “Determination of strong coupling paths at small and large interaction distances,” Grav. Cosmol., 2, 253–255 (1996).zbMATHGoogle Scholar
  22. 22.
    D. Sen, “The uncertainty of relations in quantum mechanics,” Current Sci., 107, 203–218 (2014).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.All-Russia Research Institute of Metrological Service (VNIIMS)MoscowRussia
  2. 2.National Research Center Kurchatov InstituteMoscowRussia

Personalised recommendations