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Path integral quantization of the dynamics of a classical point particle with intrinsic spin

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Il Nuovo Cimento B (1971-1996)

Summary

A quantum theory is derivedvia path integration that possesses a fundamental joint-probability amplitude for position and four-velocity,i.e. the probabilty amplitude that a particle simultaneously has a particular four-velocity at a particular position in space-time. The uncertainity principle is not violated.

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References

  1. Chihong Chou,Dynamical equations of spinning particles: Feynman’ proof, HEP-TH 9311091, also Rockfeller University preprint 93-10-B, November 1993.

  2. Ruth R. D.,The acceleration of polarized protons, inHigh Energy Spin Physics—1982 (American Institute of Physics, New York, N.Y.) 1983.

    Google Scholar 

  3. Koutchouk J.-P.,Trajectory and closed orbit correction, inFrontiers of Particle Beams; Observation, Diagnosis and Correction (Springer-Verlag, Berlin) 1989.

    Google Scholar 

  4. Carey D. C.,The optics of charged particle beams (Harwood Academic Publishers) 1987.

  5. Jin-Ho Cho, DAcovariant formulation of classical spinning particle, HEP-TH 9402012, also KAIST-CHEP-93/10 and YUMS-93-09, 1993.

  6. Ashman J. et al., Phys. Lett. B 206 (1988) 364.

    Article  ADS  Google Scholar 

  7. Close F. E. andRoberts R. G.,Phys. Rev. Lett.B,60 (1988) 1471.

    Article  ADS  Google Scholar 

  8. Ellis J. andKarliner M.,Phys. Lett. B,213 (1988) 73.

    Article  ADS  Google Scholar 

  9. Meng Ta-Chung, P. Ji-cai, Xie Qu-bing andZhu Wei,Phys. Rev. D,40 (1989) 769.

    Article  ADS  Google Scholar 

  10. van Holten J. W.,New supersymmetries for spinning particles and black holes, HEP-TH 9310092, also NIKHEF-H 93-25, 1993.

  11. Kuzenko S. M., Lyakhovich S. L. andYu. Segal A.,A geometric model of arbitrary spin massive particle, HEP-TH 9403196 (1994).

  12. Weinberg S.,Ann. Phys. (N.Y.),194 (1989) 336.

    Article  MathSciNet  ADS  Google Scholar 

  13. Frenkel W. J.,Z. Phys.,37 (1926) 243.

    Article  ADS  MATH  Google Scholar 

  14. Thomas L. H.,Philos. Mag.,3 (1927) 1.

    Article  MATH  Google Scholar 

  15. Bhaba H. J. andCorben H. C.,Proc. R. Soc. London, Ser. A,178 (1941) 243.

    Article  ADS  Google Scholar 

  16. Proca A.,J. Phys. Radium,15 (1954) 65.

    Article  MathSciNet  MATH  Google Scholar 

  17. Froissart M. andStora R.,Nucl. Instrum. Methods,7 (1960) 297.

    Article  ADS  Google Scholar 

  18. Schiller R.,Phys. Rev.,125 (1962) 1116;128 (1962) 1402.

    Article  MathSciNet  ADS  Google Scholar 

  19. Hanson A. J. andRegge T.,Ann. Phys. (N.Y.),87 (1974) 498.

    Article  MathSciNet  ADS  Google Scholar 

  20. Barut A. O.,Electrodynamics and Classical Field Theory of Field and Particles, 2nd edition (Dover, New York, N.Y.) 1980.

    Google Scholar 

  21. Bowlin J. B. andGoldhaber A. S.,J. Math. Phys.,31 (1990) 2305.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. Jackson J. D.,Classical Electrodynamics, 2nd edition (Wiley, New York, N.Y.) 1975, p. 559.

    MATH  Google Scholar 

  23. Hagedorn R.,Relativistic Kinematics (Benjamin) 1973.

  24. Nash P. L.,J. Math. Phys.,25 (1984) 2104.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. Nash P. L.,Nuovo Cimento B,105 (1990) 31.

    Article  MathSciNet  ADS  Google Scholar 

  26. Dirac P. A. M.,J. Math. Phys.,4 (1903) 901.

    Article  MathSciNet  ADS  Google Scholar 

  27. Nash P. L.,Nuovo Cimento B,107 (1992) 1291.

    Article  ADS  Google Scholar 

  28. Nash P. L.,J. Math. Phys.,21 (1980) 2534.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. Nash P. L.,J. Math. Phys.,27 (1986) 1185.

    Article  MathSciNet  ADS  Google Scholar 

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Nash, P.L. Path integral quantization of the dynamics of a classical point particle with intrinsic spin. Nuov Cim B 110, 913–926 (1995). https://doi.org/10.1007/BF02722860

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  • DOI: https://doi.org/10.1007/BF02722860

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