Standing Waves in the Lorentz-Covariant World
When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is largely because of the emergence of quantum mechanics with wave-particle duality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have to deal with Lorentz transformations of waves. We now have some nderstanding of plane waves or running waves in the covariant picture, but we do not yet have a clear picture of standing waves. In this report, we show that there is one set of standing waves which can be Lorentz-transformed while being consistent with all physical principle of quantum mechanics and relativity. It is possible to construct a representation of the Poincaré group using harmonic oscillator wave functions satisfying space-time boundary conditions. This set of wave functions is capable of explaining the quantum bound state for both slow and fast hadrons. In particular it can explain the quark model for hadrons at rest, and Feynman’s parton model hadrons moving with a speed close to that of light.
KeywordsLorentz covariance standing waves bound states relativistic quantum mechanics.
Unable to display preview. Download preview PDF.
- Kim, Y. S., Noz, M. E. 1986Theory and Applications of the Poincaré GroupReidelDordrechtGoogle Scholar
- R. P. Feynman , invited paper presented at the 1970 Washington meeting of the American Physical Society held at the Shoreham Hotel, Washington, DC, U.S.A. (April 1970).Google Scholar
- The basic difficulty with using plane waves for bound-state problems had been noted earlier in connection with the the calculation of the neutron-proton mass difference by Dashen and Frautschi. See R. F. Dashen and S. C. Frautschi, Phys. Rev. 135, B1190 and B1196 (1964); F. J. Dyson, Phys. Today 18, No. 6, 21 (1965); Y. S. Kim, Phys. Rev. 142, 1150 (1966).Google Scholar
- R. P. Feynman, The Behavior of Hadron Collisions at Extreme Energies, in High Energy Collisions, Proceedings of the Third International Conference, Stony Brook, New York, C. N. Yang et al., eds. (Gordon and Breach, New York, 1969) pp. 237–249.Google Scholar