Abstract
The uncertainty relation can be stated in terms of an area in phase space in the Wigner phase space representation of quantum mechanics. Since Lorentz boosts are area-preserving canonical transformations in the phase space of the light-cone variables, it is possible to state the uncertainty relation in a Lorentz-invariant manner. It is shown that Feynman’s parton picture is one of the observable effects of this Lorentz-invariant uncertainty relation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Wigner, E. (1932) “On the quantum correction for thermodynamic equilibrium”, Phys. Rev. 40, 749–759;
Hillery, M., O’Connell, R. F., Scully, M. O., and Wigner, E. P. (1984) “Distribution functions in physics: Fundamentals”, Phys. Rep. 106, 121–167.
Kim, Y. S. and Wigner, E. P. (1988) “Covariant phase space representation for harmonic oscillators”, Phys. Rev. A 36, 1159–1167.
Lee, H. W. (1982) “Spreading of a free wave packet”, Am. J. Phys. 50, 438–440;
Littlejohn, R. G. (1986) “The semiclassical evolution of wave packets”, Phys. Rep. 138, 193–291;
Royer, A. (1987) “Squeezed states and their Wigner functions” in Y. S. Kim and W. W. Zachary (eds.), The Physics of Phase Space, Springer-Verlag, Heidelberg, 1987, pp. 235–237.
Fujimura, K., Kobayashi, T., and Namiki, M. (1970) “Nucleon electromagnetic form factors at high momentum transfers in an extended particle model based on the quark model”, Prog. Theor. Phys. 43, 73–79.
Feynman, R. P., Kislinger, M, and Ravndal, F. (1971) “Current matrix element from a relativistic quark model”, Phys. Rev. D 3, 2706–2732.
Feynman, R. P. (1969) “The behavior of hadron collisions at extreme energies”, in C. N. Yang et al. (eds.), High Energy Collisions, Gordon and Breach, New York, pp. 237–258.
Kim, Y. S. and Noz, M. E. (1986) Theory and Applications of the Poincaré Group, Reidel Publishing Co., Dordrecht.
Hussar, P. E. (1981) “Valons and harmonic oscillators”, Phys. Rev. D 23, 2781–1983;
Haberman, M. L. and Hussar, P. E. (1988) “Reexamination of SU(6) symmetry breaking in high-energy phenomenology”, Z. Phys. C 40, 152–162.
Han, D, Kim, Y. S., and Noz, M. E. (1987) “Linear canonical transformations of coherent and squeezed states in the Wigner Phase Space”, Phys. Rev. A 37, 807–814.
Noz, M. E. and Kim, Y. S. (1988) Special Relativity and Quantum Theory, Kluwer Academic Publishers, Dordrecht.
Dirac, P. A. M. (1945) “Unitary representations of the Lorentz group”, Proc. Roy. Soc. (London) A183, 284–295.
Yukawa, H. (1953) “Structure and mass spectrum of elementary particles II. Oscillator model”, Phys. Rev. 91, 415–1945.
Dirac, P. A. M. (1927) “The quantum theory of the emission and absorption of radiation”, Proc. Roy. Soc. (London) A114, 243–265.
Dirac, P. A. M. (1949) “Forms of relativistic dynamics”, Rev. Mod. Phys. 21, 392–399.
Wigner, E. (1939) “On unitary representations of the inhomogeneous Lorentz group”, Ann. Math. 40, 149–204.
Han, D., Kim, Y. S., and Son, D. (1986) “Eulerian parametrization of Wigner’s little groups and gauge transformations in terms of rotations in two-component spinors”, J. Math. Phys. 27, 2228–2235;
Kim, Y. S. and Wigner, E. P. (1987) “Cylindrical group and massless particles” J. Math. Phys. 28, 1175–1179.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Kim, Y.S. (1989). Observable Effects of the Uncertainty Relations in the Covariant Phase Space Representation of Quantum Mechanics. In: Kafatos, M. (eds) Bell’s Theorem, Quantum Theory and Conceptions of the Universe. Fundamental Theories of Physics, vol 37. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0849-4_21
Download citation
DOI: https://doi.org/10.1007/978-94-017-0849-4_21
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4058-9
Online ISBN: 978-94-017-0849-4
eBook Packages: Springer Book Archive