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Generalized Lagrangians and Spinning Particles

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Abstract

We show that the spin structure of elementary particles can be naturally described by the generalized Ostrogradskii Lagrangians depending on higher-order derivatives. One component of a spin is related to the rotation of a particle and the other one, caused by the dependence of a Lagrangian on the acceleration, is known as a zitterbewegung component of spin.

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REFERENCES

  1. R. Dugas, A History of Mechanics, Dover, New York (1988).

    Google Scholar 

  2. J. L. Lagrange, Mécanique Analytique, Vol. 1, Courcier, Paris (1811).

    Google Scholar 

  3. M. Ostrogradskii, Mem. Acad. St. Petersburg, 6 (4), 385 (1850).

    Google Scholar 

  4. P. A. M. Dirac, “The quantum theory of the electron,” Proc. Roy. Soc. London A, 117, 610; 118, 351 (1928).

    Google Scholar 

  5. P. A. M. Dirac, The Principles of Quantum Mechanics, Oxford Univ. Press, Oxford (1967).

    Google Scholar 

  6. M. Rivas, “Classical particle systems: I. Galilei free particles,” J. Phys A., 18, 1971 (1985).

    Google Scholar 

  7. M. Rivas, “Classical relativistic spinning particles,” J. Math. Phys., 30, 318 (1989).

    Google Scholar 

  8. M. Rivas, Kinematical Theory of Spinning Particles, Kluwer, Dordrecht (2001).

    Google Scholar 

  9. E. P. Wigner, Ann. Math., 40, 149 (1939).

    Google Scholar 

  10. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures of Physics, Vol. 3, Addison-Wesley, Reading, MA (1965).

    Google Scholar 

  11. J. M. Levy-Leblond, “Group theoretical foundations of classical mechanics: The Lagrangian gauge problem,” Commun. Math. Phys., 12, 64 (1969).

    Google Scholar 

  12. V. Bargmann, “On unitary ray representations of continuous groups,” Ann. Math., 59, No. 1 (1954).

    Google Scholar 

  13. J. M. Levy-Leblond, “Galilei group and Galilean invariance,” in: E. M. Loebl (editor), Group Theory and Its Applications, Vol. 2, Academic Press, New York (1971).

    Google Scholar 

  14. J. D. Jackson, Classical Electrodynamics, Wiley, New York (1998).

    Google Scholar 

  15. M. Rivas, J. M. Aguirregabiria, and A. Hernández, “A pure kinematical explanation of the gyromagnetic ratio g = 2 of leptons and charged bosons,” Phys. Lett. A, 257, No. 21 (1999).

    Google Scholar 

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Rivas, M. Generalized Lagrangians and Spinning Particles. Ukrainian Mathematical Journal 53, 1326–1339 (2001). https://doi.org/10.1023/A:1013355828712

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  • DOI: https://doi.org/10.1023/A:1013355828712

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