EPR experiment on system in 1998 [1] strongly hints that one should use operators and for the wavefunction (WF) of antiparticle. Further analysis on Klein-Gordon (KG) equation reveals that there is a discrete symmetry hiding in relativistic quantum mechanics (RQM) that PT=C. Here PTmeans the (newly defined) combined space-time inversion (with x→-x,t→-t), while Cthe transformation of WF Ψ between particle and its antiparticle whose definition is just residing in the above symmetry. After combining with Feshbach-Villars (FV) dissociation of KG equation (Ψ=φ+x) [2], this discrete symmetry can be rigorously reformulated by the invariance of coupling equation of φand xunder either the combined space-time inversion PT or the mass inversion (m
References
[1]
Apostolakis, et al., (CPLEAR Collaboration) Physics Letters B, Vol. 422, 1998, pp. 339-348.
doi:10.1016/S0370-2693(97)01545-1
[2]
H. Feshbach and F. Villars, Review of Modern Physics, Vol. 30, 1958, pp. 24-45.
doi:10.1103/RevModPhys.30.24
[3]
T. D. Lee and C. N. Yang, Physical Review, Vol. 104, 1956, pp. 254-258.
[4]
T. D. Lee and C. N. Yang, ibid, Vol. 105, 1957, pp. 1671-1675.
[5]
T. D. Lee, R. Oehme and C. N. Yang, ibid, Vol. 106, 1957, pp. 340-345.
[6]
C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hoppes and R. P. Hudson, Physical Review, Vol. 105, 1957, pp. 1413-1415. doi:10.1103/PhysRev.105.1413
[7]
J. H. Christensen, J. W. Cronin, V. L. Fitch and R. Turlay, Physical Review Letters, Vol. 13, 1964, pp. 138-140.
doi:10.1103/PhysRevLett.13.138
[8]
K. R. Schubert, B. Wolff, J.-M. Gaillard, M. R. Jane, T. J. Ratcliffe and J.-P. Repellin, Physics Letters B, Vol. 31, 1970, pp. 662-665. doi:10.1016/0370-2693(70)90029-8
[9]
J. Beringer, et al., (Particle Data Group) Physical Review D, Vol. 86, 2012, Article ID: 010001.
doi:10.1103/PhysRevD.86.010001
[10]
G. Lüders, Kgl. Danske Vidensk. Selsk. Mat.-Fys. Medd., Vol. 28, 1954.
[11]
G. Lüders, Annals of Physics (New York), Vol. 2, 1957, pp. 1-15.
[12]
W. Pauli, “Exclusion Principle, Lorentz Group and Reflection of Space-Time and Charge,” In: W. Pauli, L. Rosenfeld and V. Weisskopf, Eds., Niels Bohr and the Development of Physics, McGraw-Hill, New York, 1955, pp. 30-51.
[13]
T. D. Lee and C. S. Wu, Annual Review of Nuclear Science, Vol. 15, 1965, pp. 381-476.
doi:10.1146/annurev.ns.15.120165.002121
[14]
A. Einstein, B. Podolsky and N. Rosen, Physical Review, Vol. 47, 1935, pp. 777-780. doi:10.1103/PhysRev.47.777
[15]
D. Bohm, “Quantum Theory,” Prentice Hall, Upper Saddle River, 1956.
[16]
J. S. Bell, Physics, Vol. 1, 1964, pp. 195-200.
[17]
H. Guan, “Basic Concepts in Quantum Mechanics,” High Education Press, Beijing, 1990.
[18]
G. J. Ni, H. Guan, W. M. Zhou and J. Yan, Chinese Physics Letters, Vol. 17, 2000, pp. 393-395.
doi:10.1088/0256-307X/17/6/002
[19]
O. Nachtmann, “Elementary Particle Physics: Concepts and Phenomena,” Springer-Verlag, Berlin, 1990.
[20]
W. Greiner and B. Müller, “Gauge Theory of Weak Interactions,” Springer-Verlag, Berlin, 1993.
[21]
E. J. Konopinski and H. M. Mahmaud, Physical Review, Vol. 92, 1953, pp. 1045-1049.
doi:10.1103/PhysRev.92.1045
[22]
G. J. Ni, Journal of Fudan University (Natural Science), No. 3-4, 1974, pp. 125-134.
[23]
G. J. Ni and S. Q. Chen, Journal of Fudan University (Natural Science), Vol. 35, 1996, pp. 325-334.
[24]
G. J. Ni and S. Q. Chen, “Relation between Space-Time Inversion and Particle-Antiparticle Symmetry and the Microscopic Essence of Special Relativity,” In: V. Dvoeglazov, Ed., Photon and Poincare Group, NOVA Science Publisher, New York, 1999, pp. 145-169.
[25]
G. J. Ni and S. Q. Chen, “Advanced Quantum Mechanics,” Rinton Press, New Jersy, 2002.
[26]
G. J. Ni, Progress in Physics, Vol. 23, 2003, pp. 484-503.
[27]
G. J. Ni, “A New Insight into the Negative-Mass Paradox of Gravity and the Accelerating Universe,” In: V. V. Dvoeglazov and A. A. Espinoza Garrido, Eds., Relativity, Gravitation, Cosmology, NOVA Science Publisher, New York, 2004, pp. 123-136.
[28]
G. J. Ni, J. J. Xu and S. Y. Lou, Chinese Physics B, Vol. 20, 2011, Article ID: 020302.
[29]
J. J. Sakurai, “Advanced Quantum Mechanics,” Addison-Wesley Publishing Company, Boston, 1978.
[30]
J. J. Sakurai, “Modern Quantum Mechanics,” John Wiley & Sons, Inc., NewYork, 1994.
[31]
J. D. Bjorken and S. D. Drell, “Relativistic Quantum Mechanics,” McGraw-Hill, New York, 1964,
[32]
J. D. Bjorken and S. D. Drell, “Relativistic Quantum Fields,” McGraw-Hill, New York, 1965.
[33]
L. B. Okun, Physics Today, Vol. 42, 1989, pp. 31-36.
[34]
G. Lochak, “De Broglie’s Initial Conception of De Broglie Waves,” In: S. Diner, D. Fargue, G. Lochak and F. Selleri, Eds., The Wave-Particle Dualism, D. Reidal Publishing Company, Dordrecht, 1984, pp. 1-25.
[35]
G. J. Ni, W. M. Zhou and J. Yan, “Comparison among Klein-Gordon Equation, Dirac Equation and Relativistic Schrodinger Equation,” In: A. E. Chubykalo, V. V. Dvoeglazov, D. J. Ernst, V. G. Kadyshevsky and Y. S. Kim, Eds., Lorentz Group, CPT and Neutrinos, World Scientific, London, 2000, pp. 68-81.
[36]
M. E. Peskin and D. V. Schroeder, “An Introdution to Quantum Field Theory,” Addison-Wesley Publishing Company, Boston, 1995.
[37]
M. Jacob and G. C. Wicks, Annals of Physics (New York), Vol. 7, 1959, pp. 404-428.
doi:10.1016/0003-4916(59)90051-X
[38]
S. Weinberg, Physical Review Letters, Vol. 19, 1967, pp. 1264-1266. doi:10.1103/PhysRevLett.19.1264
[39]
Z. Q. Shi and G. J. Ni, Chinese Physics Letters, Vol. 19, 2002, pp. 1427-1429.
[40]
Z. Q. Shi and G. J. Ni, Annales de la Fondation Louis de Bloglie, Vol. 29, 2004, pp. 1057-1066.
[41]
Z. Q. Shi and G. J. Ni, Handronic Journal, Vol. 29, 2006, pp. 401-407.
[42]
Z. Q. Shi and G. J. Ni, “Frontiers in Horizons in World Physics,” Nova Science, Marselle, 2008, pp. 53-65.
[43]
Z. Q. Shi and G. J. Ni, Modern Physics Letters A, Vol. 26, 2011, pp. 987-998. doi:10.1142/S0217732311035250
[44]
A. Cho, Science, Vol. 326, 2009, pp. 1342-1343.
doi:10.1126/science.326.5958.1342
[45]
L. H. Ryder, “Quantum Field Theory,” Cambridge University Press, Cambridge, 1996.
doi:10.1017/CBO9780511813900
[46]
T. Chang and G. J. Ni, “An Explanation of Possible Negative Mass-Square of Neutrinos,” FIZIKA B (Zagreb), Vol. 11, 2002, pp. 49-56. arXiv.org:hep-ph/0009291
[47]
G. J. Ni and T. Chang, Journal of Shaanxi Normal University (Natural Science), Vol. 30, No. 3, 2002, pp. 32-39.
[48]
G. J. Ni, Journal of Shaanxi Normal University (Natural Science), Vol. 29, No. 1, 2001, pp. 1-5.
[49]
G. J. Ni, Journal of Shaanxi Normal University (Natural Science), Vol. 30, No. 4, 2002, pp. 1-6.
[50]
G. J. Ni, “A Minimal Three-Flavor Model for Neutrino Oscillation Based on Superluminal Property,” In: V. V. Dvoeglazov and A. A. Espinoza, Eds., Relativity, Gravitation, Cosmology, NOVA Science Publisher, New York, 2004, pp. 137-148.
[51]
G. J. Ni, “Principle of Relativity in Physics and in Epistemology,” In: V. Dvoeglazov, Ed., Relativity, Gravitation, Cosmology: New Development, NOVA Science Publisher, New York, 2010, pp. 237-252.
[52]
G. J. Ni, “Cosmic Ray Spectrum and Tachyonic Neutrino,” In: V. V. Dvoeglazov and A. A. Espinoza, Eds., Relativity, Gravitation, Cosmology: New Development, NOVA Science Publisher, New York, 2010, pp. 253-265.
[53]
M. Goldhaber, L. Grodgins and A. W. Sunyar, Physical Review, Vol. 109, 1958, pp. 1015-1017.
doi:10.1103/PhysRev.109.1015
[54]
S. Weinberg, “Gravitation and Cosmology,” John Wiley, New York, 1972.
[55]
Z. M. Xu and X. J. Wu, “General Relativity and Contemporary Cosmology,” Press of Nanjing Normal University, Nanjing, 1999.
[56]
T. P. Cheng, “Relativity, Gravitation and Cosmology”, 2nd Edition, Oxford University Press, Oxford, 2010.
[57]
K. Jagannathan and L. P. S. Singh, Physical Review D, Vol. 33, 1986, pp. 2475-2477.
doi:10.1103/PhysRevD.33.2475
[58]
M. Villata, Europhysics Letters, Vol. 94, 2011, pp. 1-6.
doi:10.1209/0295-5075/94/20001
[59]
A. Kellerbauer, et al., Nuclear Instruments and Methods in Physics Research Section B, Vol. 266, 2008, pp. 351-356. doi:10.1016/j.nimb.2007.12.010
[60]
O. Klein, Zeitschrift für Physik, Vol. 53, 1929, pp. 157-165. doi:10.1007/BF01339716
[61]
W. Greiner, “Relativistic Quantum Mechanics,” Springer-Verlag, Berlin, 1990.
[62]
W. Greiner, B. Müller and J. Rafelski, “Quantum Electrodynamics of Strong Fields,” Springer-Verlag, Berlin, 1985.
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