A Semiclassical Model of Leptons

K Tennakone


A semi-classical model of leptons is presented on the assumption that they are stable equilibrium states of spherical bubble like extended structures with negative pressure of a false vacuum created inside and balanced by an outward stress due to vacuum polarization originating from the charge residing on the surface. The idea is a semiclassical analog of the Poincare model of the electron, where the outward classical electromagnetic stress is replaced by the stress due to vacuum polarization. Here the electron carries a bare mass (energy) due to negative pressure or equivalently a positive energy density inside and QED electromagnetic self-energy and both dependent on a cut-off radius R. Minimization of total energy with respect to R, yields a relation connecting equilibrium radius, negative pressure P, renormalized fine structure constant and lepton mass. Assumption that the maximum possible value of P corresponds most massive tau lepton is Planck pressure, enables determination of the renormalized fine structure constant and input of masses of the electron and muon determines corresponding internal negatives pressures and lepton radii. Tau lepton size is of the order of the Planck length and the muon and the electron are two and three orders of magnitude larger. Model suggests that the lepton flavor is an attribute associated with three different phases of a false vacuum.


Leptons; Electron self-energy; Lepton masses; Lepton flavor

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H. Murayama, Supersymmetry Phenomenology, ICTP Series in Theoretical Physics-V16, Proc. 1999 Summer School in Particle Physics, pp 298-302

M. Abraham , Prinzipien der Dynamik des Electrons, Ann. Physik, 10, 105 -179 (1903)

H.A. Lorentz , 1952 The Theory of Electrons (New York Dover)

S. Earnshaw, On the nature of the molecular forces which regulate the constitution of luminiferous ether, Trans. Camb. Phil. Soc., 7, 97-112 (1842)

M.H. Poincare, On dynamics of the electron, Rendiconti del Matematico di Palermo, 21, 129-176 (1906)

V.F. Weisskopf, On self-energy and electromagnetic field of the electron, Phys.Rev., 56, 72-85 (1939)

R.P Feynman, On space-time approach to quantum electrodynamics, Phys.Rev., 76, 769-789 (1949)

J.Schwinger J, Quantum Electrodynamics I. A Covariant Formulation, Phys.Rev., 74, 1439 (1948)

P. Gnadig , Z..Kund , P.Hasenfrats , J. Kuti Dirac’s extended electron model, Ann. Phys., 116, 380-407 (1978)

P.A.M. Dirac, An extensible model of the electron, Proc.Roy.Soc.London Ser. A, 268, 57-67 (1962)

J.L. Jimenez , I. Campos , 1999 Models of the classical electron after a century, Found. Phys. Lett., 12, 127-146 (1999)

W.B Bonner 1960 Mass of a charged sphere, Z.Phys., 160, 59-65 (1960)

R.N Tiwari ,J.R. Rao , R.R Kanakamedala , Electromagnetic mass models in general relativity, Phys. Rev.D30 489 -491(1984)

R. Gautreau R Gravitational models of a Lorentz extended electron, Phys. Rev.D, 31, 1860-1863 (1985)

C.A. Lopez Extended model of the electron in general relativity. Phys. Rev.D, 30, 313 (1984)

F.Rahaman, M.Jamil, K. Chakraborty, Revisiting the classical electron in general relativity, Astrophys. Space.Sci ,331, 191-197 (2011)

O. Grön 1986 A charged generalization of Florides interior Schwarzchild Solution, Gen. Rel.Grav., 18, 591-596 (1986)

S.K. Maurya,Y.K. Gupta,S.Ray , S.R.Chowdhury, Spherically symmetric charged compact stars, Eur.Phys.J.C 75 ,389-401 (2015)

S. Ray . S.Bhadra ,2004 Classical electron models with negative energy density in Einstein-Cartan Theory of Gravitation, Int.J.Mod. Phys. D, 13, 1555-1566 (2004)

M. Visser, A classical model for the electron, Phys.Lett. A, 139, 99 (1989)

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

T. Damour Poincare Dynamics of the electron and relativity, Competes Rendus Physique, 18, 551-52 (2017)

A. Erichorn , A. Held, C. Wetterichi., Quantum gravity predictions for the fine structure constant, arXiv: 171102949v1[hep-th] 8th Nov.2017.

H. Fritzsch, Fundamental constants at high energy, available at cds, cern.ch/record/53458/files/0201198 pdf (2001)

H. Dehmelt, A single atomic particle forever floating in free space: A new value for electron Radius, Phys. Scr. 1988 102-110 (1988)

J. Hudson , D. Kara , M.I, Smallman J, Sauer , B.R ,Tarbutt E M, E , Hinds E A, Improved measurement of the shape of the electron, Nature 473 493 (2011)


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