publication . Preprint . 1996

Field theory of the spinning electron: Internal motions

Salesi, Giovanni; Recami, Erasmo;
Open Access English
  • Published: 29 Jul 1996
Abstract
We present here a field theory of the spinning electron, by writing down a new equation for the 4-velocity field v^mu (different from that of Dirac theory), which allows a classically intelligible description of the electron. Moreover, we make explicit the noticeable kinematical properties of such velocity field (which also result different from the ordinary ones). At last, we analyze the internal zitterbewegung (zbw) motions, for both time-like and light-like speeds. We adopt in this paper the ordinary tensorial language. Our starting point is the Barut-Zanghi classical theory for the relativistic electron, which related spin with zbw. This paper is dedicated t...
Subjects
free text keywords: High Energy Physics - Theory
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[1] A.H. Compton: Phys. Rev. 14 (1919) 20, 247; E. Schr¨odinger: Sitzunger. Preuss. Akad. Wiss. Phys. Math. Kl. 24 (1930) 418. See also P.A.M. Dirac: The Principles of Quantum Mechanics, 4th edition (Claredon; Oxford, 1958), p.262; J. Frenkel: Z. Phys. 37 (1926) 243; M. Mathisson: Acta Phys. Pol. 6 (1937) 163; H. H¨onl and A. Papapetrou: Z. Phys. 112 (1939) 512; 116 (1940) 153; M.J. Bhabha and H.C. Corben: Proc. Roy. Soc. (London) A178 (1941) 273; K. Huang: Am. J. Phys. 20 (1952) 479; H. H¨onl: Ergeb. Exacten Naturwiss. 26 (1952) 29; A. Proca: J. Phys. Radium 15 (1954) 5; M. Bunge: Nuovo Cimento 1 (1955) 977; F. Gursey: Nuovo Cimento 5 (1957) 784; W.H. Bostick: “Hydromagnetic model of an elementary particle”, in Gravity Res. Found. Essay Contest (1958 and 1961), and refs. therein; H.C. Corben: Phys. Rev. 121 (1961) 1833; T.F. Jordan and M. Mukunda: Phys. Rev. 132 (1963) 1842; B. Liebowitz: Nuovo Cimento A63 (1969) 1235; H. Jehle: Phys. Rev. D3 (1971) 306; F. Riewe: Lett. Nuovo Cim. 1 (1971) 807; G.A. Perkins: Found. Phys. 6 (1976) 237; D. Gutkowski, M. Moles and J.P. Vigier: Nuovo Cim. B39 (1977) 193; A.O. Barut: Z. Naturforsch. A33 (1978) 993; J.A. Lock: Am. Lecture Notes in Physics, vol.135 (1987) 306; M. H. McGregor: The enigmatic electron (Kluwer; Dordrecht, 1992); W.A. Rodrigues, J. Vaz and E. Recami: Found. Phys. 23 (1993) 459.

[2] A.O. Barut and N. Zanghi: Phys. Rev. Lett. 52 (1984) 2009. See also A.O. Barut and A.J. Bracken: Phys. Rev. D23 (1981) 2454; D24 (1981) 3333; A.O. Barut and M. Pavsic: Class. Quantum Grav. 4 (1987) L131; A.O. Barut: Phys. Lett. B237 (1990) 436.

[3] E. Recami and G. Salesi: “Field theory of the electron: Spin and zitterbewegung”, in Particles, Gravity and Space-Time, ed. by P.I. Pronin and G.A. Sardanashvily (World Scient.; Singapore, 1996), pp.345-368.

[4] M. Pavsic, E. Recami, W.A. Rodrigues, G.D. Maccarrone, F. Raciti and G. Salesi: Phys. Lett. B318 (1993) 481.

[5] M. Pavsic: Phys. Lett. B205 (1988) 231; B221 (1989) 264; Class. Quant. Grav. 7 (1990) L187.

[6] A.O. Barut and M. Pavsic: Phys. Lett. B216 (1989) 297; F.A. Ikemori: Phys. Lett. B199 (1987) 239. See also D. Hestenes: Found. Phys. 20 (1990) 1213; S. Gull, A. Lasenby and C. Doran: “Electron paths, tunneling and diffraction in the space-time algebra”, to appear in Found. Phys. (1993); D. Hestenes and A. Weingartshofer (eds.): The electron (Kluwer; Dordrecht, 1971), in particular the contributions by H. Kru¨ger, by R. Boudet, and by S. Gull; A. Campolattaro: Int. J. Theor. Phys. 29 (1990) 141; D. Hestenes: Found. Phys. 15 (1985) 63.

[7] W.A. Rodrigues Jr., J. Vaz, E. Recami and G. Salesi: Phys. Lett. B318 (1993) 623.

[8] For the physical interpretation of the negative frequency waves, without any recourse to a “Dirac sea”, see e.g. E. Recami: Found. Phys. 8 (1978) 329; E. Recami and W.A. Rodrigues: Found. Phys. 12 (1982) 709; 13 (1983) 533; M. Pavsic and E. Recami: Lett. Nuovo Cim. 34 (1982) 357. See also R. Mignani and E. Recami: Lett. Nuovo Cim. 18 (1977) 5; A. Garuccio et al.: Lett. Nuovo Cim. 27 (1980) 60.

[9] P. Lounesto: “Clifford algebras, relativity and quantum mechanics”, in Gravitation: The Space-Time Structure - Proceedings of Silarg-VIII, ed. by W.A. Rodrigues et al. (World Scient.; Singapore, 1994).

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Abstract
We present here a field theory of the spinning electron, by writing down a new equation for the 4-velocity field v^mu (different from that of Dirac theory), which allows a classically intelligible description of the electron. Moreover, we make explicit the noticeable kinematical properties of such velocity field (which also result different from the ordinary ones). At last, we analyze the internal zitterbewegung (zbw) motions, for both time-like and light-like speeds. We adopt in this paper the ordinary tensorial language. Our starting point is the Barut-Zanghi classical theory for the relativistic electron, which related spin with zbw. This paper is dedicated t...
Subjects
free text keywords: High Energy Physics - Theory
Download from

[1] A.H. Compton: Phys. Rev. 14 (1919) 20, 247; E. Schr¨odinger: Sitzunger. Preuss. Akad. Wiss. Phys. Math. Kl. 24 (1930) 418. See also P.A.M. Dirac: The Principles of Quantum Mechanics, 4th edition (Claredon; Oxford, 1958), p.262; J. Frenkel: Z. Phys. 37 (1926) 243; M. Mathisson: Acta Phys. Pol. 6 (1937) 163; H. H¨onl and A. Papapetrou: Z. Phys. 112 (1939) 512; 116 (1940) 153; M.J. Bhabha and H.C. Corben: Proc. Roy. Soc. (London) A178 (1941) 273; K. Huang: Am. J. Phys. 20 (1952) 479; H. H¨onl: Ergeb. Exacten Naturwiss. 26 (1952) 29; A. Proca: J. Phys. Radium 15 (1954) 5; M. Bunge: Nuovo Cimento 1 (1955) 977; F. Gursey: Nuovo Cimento 5 (1957) 784; W.H. Bostick: “Hydromagnetic model of an elementary particle”, in Gravity Res. Found. Essay Contest (1958 and 1961), and refs. therein; H.C. Corben: Phys. Rev. 121 (1961) 1833; T.F. Jordan and M. Mukunda: Phys. Rev. 132 (1963) 1842; B. Liebowitz: Nuovo Cimento A63 (1969) 1235; H. Jehle: Phys. Rev. D3 (1971) 306; F. Riewe: Lett. Nuovo Cim. 1 (1971) 807; G.A. Perkins: Found. Phys. 6 (1976) 237; D. Gutkowski, M. Moles and J.P. Vigier: Nuovo Cim. B39 (1977) 193; A.O. Barut: Z. Naturforsch. A33 (1978) 993; J.A. Lock: Am. Lecture Notes in Physics, vol.135 (1987) 306; M. H. McGregor: The enigmatic electron (Kluwer; Dordrecht, 1992); W.A. Rodrigues, J. Vaz and E. Recami: Found. Phys. 23 (1993) 459.

[2] A.O. Barut and N. Zanghi: Phys. Rev. Lett. 52 (1984) 2009. See also A.O. Barut and A.J. Bracken: Phys. Rev. D23 (1981) 2454; D24 (1981) 3333; A.O. Barut and M. Pavsic: Class. Quantum Grav. 4 (1987) L131; A.O. Barut: Phys. Lett. B237 (1990) 436.

[3] E. Recami and G. Salesi: “Field theory of the electron: Spin and zitterbewegung”, in Particles, Gravity and Space-Time, ed. by P.I. Pronin and G.A. Sardanashvily (World Scient.; Singapore, 1996), pp.345-368.

[4] M. Pavsic, E. Recami, W.A. Rodrigues, G.D. Maccarrone, F. Raciti and G. Salesi: Phys. Lett. B318 (1993) 481.

[5] M. Pavsic: Phys. Lett. B205 (1988) 231; B221 (1989) 264; Class. Quant. Grav. 7 (1990) L187.

[6] A.O. Barut and M. Pavsic: Phys. Lett. B216 (1989) 297; F.A. Ikemori: Phys. Lett. B199 (1987) 239. See also D. Hestenes: Found. Phys. 20 (1990) 1213; S. Gull, A. Lasenby and C. Doran: “Electron paths, tunneling and diffraction in the space-time algebra”, to appear in Found. Phys. (1993); D. Hestenes and A. Weingartshofer (eds.): The electron (Kluwer; Dordrecht, 1971), in particular the contributions by H. Kru¨ger, by R. Boudet, and by S. Gull; A. Campolattaro: Int. J. Theor. Phys. 29 (1990) 141; D. Hestenes: Found. Phys. 15 (1985) 63.

[7] W.A. Rodrigues Jr., J. Vaz, E. Recami and G. Salesi: Phys. Lett. B318 (1993) 623.

[8] For the physical interpretation of the negative frequency waves, without any recourse to a “Dirac sea”, see e.g. E. Recami: Found. Phys. 8 (1978) 329; E. Recami and W.A. Rodrigues: Found. Phys. 12 (1982) 709; 13 (1983) 533; M. Pavsic and E. Recami: Lett. Nuovo Cim. 34 (1982) 357. See also R. Mignani and E. Recami: Lett. Nuovo Cim. 18 (1977) 5; A. Garuccio et al.: Lett. Nuovo Cim. 27 (1980) 60.

[9] P. Lounesto: “Clifford algebras, relativity and quantum mechanics”, in Gravitation: The Space-Time Structure - Proceedings of Silarg-VIII, ed. by W.A. Rodrigues et al. (World Scient.; Singapore, 1994).

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