Abstract
The Lee, Oehme and Yang (LOY) theory of time evolution in two state subspace of states of the complete system is discussed. Some inconsistencies in the assumptions and approximations used in the standard derivation of the LOY effective Hamiltonian, HLOY, governing this time evolution are found. Eliminating these inconsistencies and using the LOY method, approximate formulae for the effective Hamiltonian, H||, governing the time evolution in this subspace (improving those obtained by LOY) are derived. It is found, in contradistinction to the standard LOY result, that in the case of neutral kaons (〈K 0 |H|||K 0 〉−〈¯K 0 |H|||¯K 0 〉), cannot take the zero value if the total system the preserves CPT-symmetry. Within the use of the method mentioned above formulae for H|| acting in the three state (three dimensional) subspace of states are also found.
Similar content being viewed by others
REFERENCES
T. D. Lee, R. Oehme, and C. N. Yang, Phys. Rev. 106, 340 (1957).
T. D. Lee and C. S. Wu, Annual Review of Nuclear Science 16, 471 (1966).
M. K. Gaillard and M. Nikolic, eds., Weak Interactions (INPN et de Physique des Particules, Paris, 1977); Chap. 5, Appendix A.
S. M. Bilenkij, Particles and Nucleus, Vol. 1, No. 1 (Dubna 1970), p. 227 [in Russian]. P. K. Kabir, The CP-Puzzle (Academic Press, New York, 1968).
J. W. Cronin, Rev. Mod. Phys. 53, 373 (1981). J. W. Cronin, Acta Phys. Polon. B 15, 419 (1984). V. V. Barmin et al., Nucl. Phys. B 247, 293 (1984). L. Lavoura, Ann. Phys. (NY) 207, 428 (1991). C. Buchanan et al., Phys. Rev. D 45, 4088 (1992). C. O. Dib and R. D. Peccei, Phys. Rev. D 46, 2265 (1992). R. D. Peccei, “CP and CPT violation: Status and prospects,” Preprint UCLA- 93- TEP- 19 (University of California, June 1993).
E. D. Comins and P. H. Bucksbaum, Weak Interactions of Leptons and Quarks (Cambridge University Press, 1983). T. P. Cheng and L. F. Li, Gauge Theory of Elementary Particle Physics (Clarendon, Oxford 1984).
L. Maiani, in The Second Da8ne Physics Handbook, Vol. 1, L. Maiani, G. Pancheri, and N. Paver, eds. (SIS-Pubblicazioni, INFN-LNF, Frascati, 1995), pp. 3–26.
L. A. Khalfin, “Theory of unstable neutrino mixing and the 17 keV neutrino problem,” preprint HU-TFT-92-21 (Helsinki, June 1992).
M. Caldo-Ceolin, “Neutron- antineutron oscillation experiments,” Proceedings of the International Conference of Unified Theories and Their Experimental Tests (Venice, March 16- 18, 1982); “Sensitive search for neutron- antineutron transitions at the ill reactor,” AIP Conference Proceedings No. 125 of the Fifth International Symposium on “Capture Gamma- Ray Spectroscopy and Related Topics,” S. Raman, ed. (Knoxville, September 1984), p. 871.
L. A. Khalfin, “The theory of K0, K- 0 (D0, D- 0 and T0, T- 0) mesons beyond the Weisskopf- Wigner approximation and the CP-problem,” preprint LOMI P-4-80 (Leningrad, February 1980).
L. A. Khalfin, Foundations of Physics 27, 1549 (1997).
L. A. Khalfin, Preprints of the CPT, The University of Texas at Austin: DOE-ER-40200-211, February 1990 and DOE-ER-40200-247, February 1991; (unpublished, cited in Ref. 13), and references one can find therein.
C. B. Chiu and E. C. G. Sudarshan, Phys. Rev. D 42, 3712 (1990).
E. C. G. Sudarshan, C. B. Chiu, and G. Bhamathi, “Unstable systems in generalized quan-tum theory,” preprint DOE-40757-023 and CPP-93-23 (University of Texas, October 1993).
K. Urbanowski, Phys. Lett. B 313, 374 (1993).
K. Urbanowski, “Is the new interpretation of some standard CPT-violation parameters necessary?,” preprint of the Pedagogical University, No. WSP-IF 94-39 (Zielona Gora, May 1994); “CPT transformation properties of the exact effective Hamiltonian for neutral Kaon complex,” preprint of the Pedagogical University, No. WSP-IF 96- 44 (Zielona Gora, March 1996); “CPT transformation properties of the exact effective Hamiltonian for neutral Kaon and similar complexes,” preprint of the Pedagogical University, No. WSP-IF 97-50 (Zielona Gora, July 1997), hep-ph- 9803376.
K. Urbanowski, Int. J. Mod. Phys. A 13, 965 (1998).
K. Urbanowski, “Why the LOY model cannot be used for designing CPT-invariance tests in neutral Kaons systems? On CPT-noninvariance of systems with exponentially decaying particles,” preprint of the Pedagogical University, No. WSP-IF 94-38 (Zielona Gora, May 1994).
T. Mochizuki, N. Hashimoto, A. Shinobori, and S. Y. Tsai, “Remarks on theoretical frameworks describing the neutral Kaon system,” preprint of The Nihon University, No. NUP-A-97-14 (Tokyo, June 1997).
V. F. Weisskopf and E. T. Wigner, Z. Phys. 63, 54 (1930); 65, 18 (1930).
P. K. Kabir and A. Pilaftsis, Phys. Rev. A 53, 66 (1966).
W. Pauli, in Niels Bohr and the Development of Physics, W. Pauli, ed. (Pergamon Press, London, 1955), pp. 30–51. G. Luders, Ann. Phys. (NY) 2, 1 (1957). R. Jost, Helv. Phys. Acta 30, 409 (1957). R. F. Streater and A. S. Wightman, CPT, Spin, Statistics and All That (Benjamin, New York, 1964). N. N. Bogolubov, A. A. Logunov, and I. T. Todorov, Introduction to Axiomatic Field Theory (Benjamin, New York, 1975).
A. Messiah, Quantum Mechanics, Vol. 2 (Wiley, New York, 1966).
A. Bohm, Quantum Mechanics: Foundations and Applications, 2nd edn. (Springer, New York 1986).
K. Urbanowski, Int. J. Mod. Phys. A 10, 1151 (1995).
e.g., R. Zwanzig, Physica 30, (1964), 1109. F. Haake, Statistical Treatment of Open Systems by Generalized Master Equations, Springer Tracts in Modern Physics, Vol. 66 (Springer, Berlin, 1973). L. P. Horwitz and J. P. Marchand, Rocky Mount. J. Math. 1, 225 (1971). E. B. Davis, Quantum Theory of Open System (Academic, London, 1976).
W. Krolikowski and J. Rzewuski, Bull. Acad. Polon. Sci. 4, 19 (1956).
W. Krolikowski and J. Rzewuski, Nuovo. Cim. B 25, 739 (1975) and references therein.
K. Urbanowski, Acta Phys. Polon. B 14, 485 (1983).
K. Urbanowski, Int. J. Mod. Phys. A 8, 3721 (1993).
K. Urbanowski, Phys. Rev. A 50, 2847 (1994).
E. Cohen and L. P. Horwitz, preprints No. hep-ph- 9808030, hep-ph- 9811332.
L. K. Gibbons et al., “CP and CPT symmetry tests from the two-pion decays of the neutral Kaon with the Fermilab-E731 detector,” preprints FERMILAB-Pub-95- 392-E, EFI-95-76; Phys. Rev. D 55, 6625 (1997).
J. Ellis, J. L. Lopez, N. E. Mavratos, and D. V. Nanopulous, Phys. Rev. D 53, 3846 (1996); J. Ellis, N. E. Mavratos, and D. V. Nanopulous, Phys. Lett. B 293, 142 (1992); V. A. Kostelecky, Phys. Rev. Lett. 80, 1818 (1998).
E. Fischbach and C. Talmadge, Nature 356, 207 (1992). E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge, and S. H. Aronson, Phys. Rev. Lett. 56, 3 (1986). D. Sudarsky, E. Fischbach, C. Talmadge, A. H. Aronson, and H.-Y. Cheng, Ann. Phys. (NY) 207, 103 (1991). E. Fischbach and C. Talmadge, preprint No. hep-ph- 9606249.
T. Haymbye, R. B. Mann, and U. Sarkar, Phys. Lett. B 421, 105 (1998). T. Haymbye, R. B. Mann, and U. Sarkar, Phys. Rev. D 58, (1998), Art. no. 025003. C. Alvarez and R. B. Mann, Phys. Rev. D 55, 1732 (1997). R. J. Hughes, Phys. Rev. D 46, R2283 (dy1992). I. R. Kenyon, Phys. Lett. B 237, 274 (1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Urbanowski, K., Piskorski, J. On Departures from the Lee, Oehme and Yang Approximation. Foundations of Physics 30, 839–866 (2000). https://doi.org/10.1023/A:1003698323985
Issue Date:
DOI: https://doi.org/10.1023/A:1003698323985