27-3-2006
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Papers downloadable from this site, classified according to topic. (By chronological order, see here)

(The section where the considered thema appears in the paper is specified).


 

GENERALIZED SCALE LAWS


QUANTUM MECHANICS


FIELD THEORY


APPLICATIONS IN PARTICLE PHYSICS AND HIGH ENERGY PHYSICS


APPLICATIONS IN ASTROPHYSICS AND SCIENCES OF THE UNIVERSE


APPLICATIONS IN SCIENCES OF LIFE AND HUMAN SCIENCES

GENERALIZED SCALE LAWS
 

  • Nottale, L., 1997, in "Scale invariance and beyond", proceedings of Les Houches school, Ed. B. Dubrulle, F. Graner and D. Sornette, (EDP Sciences / Springer), p. 249  (PDF)

    •  "Scale relativity"
     
  • Nottale L., 2002, in Traité IC2, Traitement du Signal et de l'Image, "Lois d'échelle, fractales et ondelettes", sous la direction de P. Abry, P. Gonçalvès et J. Levy Vehel  (Hermès Lavoisier 2002), Vol. 2, Chap. 7, pp. 233-265. (PDF)

    •  "Relativité d'échelle, nondifférentiabilité et espace-temps fractal" (in French)
    REVIEW PAPER

    Special scale-relativity ("log-Lorentzian" dilation laws)
     

  • Nottale, L., 1992, Int. J. Mod. Phys. A7, 4899-4936  (completed by notes and errata) (PDF)

    • "The theory of scale relativity".
     
  • Nottale, L., 1994, Chaos, Solitons & Fractals, 4, 361-388.  (PostScript) (PDF)

    • Reprinted in "Quantum Mechanics, Diffusion and Chaotic Fractals", Eds. M.S. El Naschie, O.E. Rössler and I. Prigogine (Pergamon, 1995), p. 51
    "Scale-Relativity, Fractal Space-Time and Quantum Mechanics".
    Sec. 5
     
  • Nottale, L., 1995,   Chaos, Solitons & Fractals  6, 399.    (PDF)

    •  "Scale-Relativity: From Quantum Mechanics to Chaotic Dynamics".
    Sec. 4
     
  • Nottale, L., 1996, Chaos, Solitons and Fractals, 7, 877-938  (PostScript)  (PDF)

    •  "Scale Relativity and Fractal Space-Time: Application to Quantum Physics, Cosmology and  Chaotic systems"
    Sec. 2.3

    Scale Dynamics
     

  • Nottale, L., 1997, in "Scale invariance and beyond", proceedings of Les Houches school, Ed. B. Dubrulle, F. Graner and D. Sornette, (EDP Sciences / Springer), p. 249  (PDF)

    •  "Scale relativity"
     
  • Nottale L., 2002, in Traité IC2, Traitement du Signal et de l'Image, "Lois d'échelle, fractales et ondelettes", sous la direction de P. Abry, P. Gonçalvès et J. Levy Vehel  (Hermès Lavoisier 2002), Vol. 2, Chap. 7, pp. 233-265. (PDF)

    •  "Relativité d'échelle, nondifférentiabilité et espace-temps fractal" (in French)
    Sec. 7.5.5

    Log-periodic scale laws, discrete scale invariance
     

  • Nottale, L., Chaline, J., & Grou, P., 2001, in "Fractals in Biology and Medicine", Vol III, Proceedings of Fractal 2000 Third International Symposium, Eds. G. Losa, D. Merlini, T. Nonnenmacher and E. Weibel, Birckhäuser Verlag, p. 247.

    •  "On the fractal structure of evolutionary trees"     (PDF)
    Sec. 2
     
  • Nottale L., 2002, in Traité IC2, Traitement du Signal et de l'Image, "Lois d'échelle, fractales et ondelettes", sous la direction de P. Abry, P. Gonçalvès et J. Levy Vehel  (Hermès Lavoisier 2002), Vol. 2, Chap. 7, pp. 233-265. (PDF)

    •  "Relativité d'échelle, nondifférentiabilité et espace-temps fractal" (in French)
    Sec. 7.5.3

    QUANTUM MECHANICS

    Non relativistic quantum mechanics (Schrödinger equation)
     

  • Nottale, L., 1993, (World Scientific, 1993), (LIVRE, 347 pp.) (PDF)

    • "Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity."
    Chap. 5.6
     
  • Nottale, L., 1994, Chaos, Solitons & Fractals, 4, 361-388.  (PostScript) (PDF)

    • Reprinted in "Quantum Mechanics, Diffusion and Chaotic Fractals", Eds. M.S. El Naschie, O.E. Rössler and I. Prigogine (Pergamon, 1995), p. 51
    "Scale-Relativity, Fractal Space-Time and Quantum Mechanics"
    Secs. 2, 4
     
  • Nottale, L., 1995,  invited conference in "Chaos and diffusion in Hamiltonian systems", Proceedings of the fourth workshop in Astronomy and Astrophysics of Chamonix (France), 7-12 February 1994, Ed. D. Benest et C. Froeschlé, (Editions Frontières), pp. 173-198.  (PDF)

    •  "New Formulation of Stochastic Mechanics. Application to Chaos".
     
  • Nottale, L., 1996, Chaos, Solitons and Fractals, 7, 877-938  (PostScript)  (PDF)

    •  "Scale Relativity and Fractal Space-Time: Application to Quantum Physics, Cosmology and  Chaotic systems"
    Secs. 4
     
  • Nottale L., 1997, Astron. Astrophys., 327, 867.    (PostScript) (PDF)

    • "Scale relativity and  Quantization of the Universe. I. Theoretical framework"
     
  • Nottale L., 2002, in Traité IC2, Traitement du Signal et de l'Image, "Lois d'échelle, fractales et ondelettes", sous la direction de P. Abry, P. Gonçalvès et J. Levy Vehel  (Hermès Lavoisier 2002), Vol. 2, Chap. 7, pp. 233-265. (PDF)

    •  "Relativité d'échelle, nondifférentiabilité et espace-temps fractal" (in French)
    Sec. 7.6
     
  • Nottale L., 2004, contribution invitée à CASYS'03, Sixth International Conference  on Computing Anticipatory Systems (Liège, Belgique, Aout 2003), à l'occasion de la remise du CASYS Award. AIP Conference proceedings, 718, 68  (PDF)

    • "The Theory of Scale Relativity: Non-Differentiable Geometry and Fractal Space-Time"
    Sec. 3

    Relativistic quantum mechanics

    Klein-Gordon equation
  • Nottale, L., 1994, invited conference in "Relativity in General", (1993 Spanish Relativity Meeting), Salas, Ed. J. Diaz Alonso and M. Lorente Paramo (Frontières), pp.121-132.  (PDF)

    •  "Scale-Relativity: First Steps toward a Field Theory."
    Sec. 2.2
     
  • Nottale, L., 1996, Chaos, Solitons and Fractals, 7, 877-938  (PostScript)  (PDF)

    •  "Scale Relativity and Fractal Space-Time: Application to Quantum Physics, Cosmology and  Chaotic systems"
    Sec. 5.1
     
  • Nottale L., 2004, contribution invitée à CASYS'03, Sixth International Conference  on Computing Anticipatory Systems (Liège, Belgique, Aout 2003), à l'occasion de la remise du CASYS Award. AIP Conference proceedings, 718, 68  (PDF)

    • "The Theory of Scale Relativity: Non-Differentiable Geometry and Fractal Space-Time"
    Sec. 5.1
    Dirac equation
  • Célérier M.N. & Nottale L., 2003, Electromagnetic Phenomena, T. 3, N°1 (9), 83, special issue dedicated to the  75th anniversary of the discovery of the Dirac equation  (arXiv:hep-th/0210027)

    • "A scale-relativistic derivation of the Dirac Equation"
     
  • Célérier M.N. & Nottale L., 2004, J. Phys. A 37, 931-955  (PDF)

    • "Quantum-classical transition in scale relativity"
     
  • Nottale L., 2004, invited contribution in CASYS'03, Sixth International Conference  on Computing Anticipatory Systems (Liège, Belgium, August 2003). To appear in: AIP Conference Proceedings (PDF)

    • "The Theory of Scale Relativity: Non-Differentiable Geometry and Fractal Space-Time"
    Sec. 5.2

    Quantum mechanics in scale space, complexergy
     

  • Nottale L., 2004, invited contribution in CASYS'03, Sixth International Conference  on Computing Anticipatory Systems (Liège, Belgium, August 2003). To appear in: AIP Conference Proceedings (PDF)

    • "The Theory of Scale Relativity: Non-Differentiable Geometry and Fractal Space-Time"
    Sec. 6

    FIELD THEORY

    Electromagnetism, Abelian gauge fields
     

  • Nottale, L., 1994, invited conference in "Relativity in General", (1993 Spanish Relativity Meeting), Salas, Ed. J. Diaz Alonso and M. Lorente Paramo (Frontières), pp.121-132.  (PDF)

    •  "Scale-Relativity: First Steps toward a Field Theory".
     
  • Nottale, L., 1996, Chaos, Solitons and Fractals, 7, 877-938  (PostScript)  (PDF)

    •  "Scale Relativity and Fractal Space-Time: Application to Quantum Physics, Cosmology and  Chaotic systems"
    Secs. 5.2, 5.3, 6.3
     
  • Nottale L., 2002, in Traité IC2, Traitement du Signal et de l'Image, "Lois d'échelle, fractales et ondelettes", sous la direction de P. Abry, P. Gonçalvès et J. Levy Vehel  (Hermès Lavoisier 2002), Vol. 2, Chap. 7, pp. 233-265. (PDF)

    •  "Relativité d'échelle, nondifférentiabilité et espace-temps fractal" (in French)
    Sec. 7.5.7
     
  • Nottale L., 2003, Electromagnetic Phenomena T. 3, N°1 (9), 24, numéro spécial dédié au 75è anniversaire de la découverte de l'équation de Dirac.  (PDF)

    • "Theory of Electron in Scale Relativity"

    Non-Abelian gauge fields
     

  • Nottale L., Célérier M.N. & Lehner T., 2006,  J. Math. Phys. 47, 032303 (arXiv:hep-th/0307093)   (PDF)

    • "Non Abelian gauge field theory in scale relativity"
     
  • Nottale L., 2004, invited contribution  in the volume "Progress in Field Theory Research", (Nova Science 2005), accepted for publication  (PDF)

    • "Geometric interpretation of gauge fields in the theory of scale relativity"


     

    APPLICATIONS IN PARTICLE PHYSICS AND HIGH ENERGY PHYSICS

    Coupling constants (charges)
     

  • Nottale, L., 1992, Int. J. Mod. Phys. A7, 4899-4936  (completed by notes and errata) (PDF)

    • "The theory of scale relativity".
    Sec. 9
     
  • Nottale, L., 1994, Chaos, Solitons & Fractals, 4, 361-388.  (PostScript) (PDF)

    • Reprinted in "Quantum Mechanics, Diffusion and Chaotic Fractals", Eds. M.S. El Naschie, O.E. Rössler and I. Prigogine (Pergamon, 1995), p. 51
    "Scale-Relativity, Fractal Space-Time and Quantum Mechanics"
    Sec. 5
     
  • Nottale, L., 1996, Chaos, Solitons and Fractals, 7, 877-938  (PostScript)  (PDF)

    •  "Scale Relativity and Fractal Space-Time: Application to Quantum Physics, Cosmology and  Chaotic systems"
    Sec. 6.1

    Mass-coupling relations (mass - charge)
     

  • Nottale, L., 1994, invited conference in "Relativity in General", (1993 Spanish Relativity Meeting), Salas, Ed. J. Diaz Alonso and M. Lorente Paramo (Frontières), pp.121-132.  (PDF)

    •  "Scale-Relativity: First Steps toward a Field Theory".
     
  • Nottale, L., 1996, Chaos, Solitons and Fractals, 7, 877-938  (PostScript)  (PDF)

    •  "Scale Relativity and Fractal Space-Time: Application to Quantum Physics, Cosmology and  Chaotic systems"
    Sec. 6.3

    Mass and charge spectrum of elementary particles
     

  • Nottale, L., 1994, Chaos, Solitons & Fractals, 4, 361-388.  (PostScript) (PDF)

    • Reprinted in "Quantum Mechanics, Diffusion and Chaotic Fractals", Eds. M.S. El Naschie, O.E. Rössler and I. Prigogine (Pergamon, 1995), p. 51
    "Scale-Relativity, Fractal Space-Time and Quantum Mechanics"
    Sec. 6
     
  • Nottale, L., 1995,   Chaos, Solitons & Fractals  6, 399.    (PDF)

    •  "Scale-Relativity: From Quantum Mechanics to Chaotic Dynamics".
    Sec. 5
     
  • Nottale, L., 1996, Chaos, Solitons and Fractals, 7, 877-938  (PostScript)  (PDF)

    •  "Scale Relativity and Fractal Space-Time: Application to Quantum Physics, Cosmology and  Chaotic systems"
    Sec. 6.2

    APPLICATIONS IN ASTROPHYSICS AND SCIENCES OF THE UNIVERSE

    Cosmology
     

  • Nottale, L., 1996, Chaos, Solitons and Fractals, 7, 877-938  (PostScript)  (PDF)

    •  "Scale Relativity and Fractal Space-Time: Application to Quantum Physics, Cosmology and  Chaotic systems"
    Sec. 7
     
  • Nottale, L., 1998, Ciel et Terre, Bulletin de la Société royale belge d'Astronomie, vol 114 (2), 63-71.  (PDF)

    • "Relativité d'échelle et cosmologie" (in French)
     
  • Nottale L., 2003, Chaos Solitons and Fractals, 16, 539 (PostScript) ou (PDF)

    • "Scale-relativistic cosmology"
    REVIEW PAPER

    Cosmological Constant
     

  • Nottale, L., 1993, (World Scientific, 1993), 333 pp.

    • "Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity."
    Chapter 7.1: "Scale Relativity and Cosmology", pp. 283-307 (PDF)
     
  • Nottale, L., 1996, Chaos, Solitons and Fractals, 7, 877-938  (PostScript)  (PDF)

    •  "Scale Relativity and Fractal Space-Time: Application to Quantum Physics, Cosmology and  Chaotic systems"
    Sec. 7.1
     
  • Nottale, L., 1998, Ciel et Terre, Bulletin de la Société royale belge d'Astronomie, vol 114 (2), 63-71.  (PDF)

    • "Relativité d'échelle et cosmologie" (in French)
     
  • Nottale L., 2003, Chaos Solitons and Fractals, 16, 539 (PostScript) ou (PDF)

    • "Scale-relativistic cosmology"  (REVIEW PAPER)
    Sec. 3.6

    Formation and evolution of structures
     

  • Nottale, L., 1993, (World Scientific, 1993), (Livre, 333 pp.)

    • "Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity."
    Chapter 7.2: "Beyond Chaos", pp. 307-321   (PDF)
     
  • Nottale, L., 1996, Chaos, Solitons and Fractals, 7, 877-938  (PostScript)  (PDF)

    •  "Scale Relativity and Fractal Space-Time: Application to Quantum Physics, Cosmology and  Chaotic systems"
    Sec. 7.2
     
  • Nottale L., 1997, Astron. Astrophys., 327, 867.    (PostScript) (PDF)

    • "Scale relativity and  Quantization of the Universe. I. Theoretical framework"
     
  • Da Rocha D. & Nottale L., 2003, Chaos Solitons and Fractals, 16, 565  (PDF) (arXiv:astro-ph/0310036)

    • "Gravitational structure formation in scale relativity"
    REVIEW PAPER

    Solar system
     

  • Nottale, L., 1993, (World Scientific, 1993), (Livre, 333 pp.)

    • "Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity."
    Chapter 7.2: "Beyond Chaos", pp. 307-321   (PDF)
     
  • Nottale, L., 1995,  invited conference in "Chaos and diffusion in Hamiltonian systems", Proceedings of the fourth workshop in Astronomy and Astrophysics of Chamonix (France), 7-12 February 1994, Ed. D. Benest et C. Froeschlé, (Editions Frontières), pp. 173-198.  (PDF)

    •  "New Formulation of Stochastic Mechanics. Application to Chaos".
     
  • Nottale, L., 1995,   Chaos, Solitons & Fractals  6, 399.    (PDF)

    •  "Scale-Relativity: From Quantum Mechanics to Chaotic Dynamics".
    Sec. 6
     
  • Nottale, L., 1996, Chaos, Solitons and Fractals, 7, 877-938  (PostScript)  (PDF)

    •  "Scale Relativity and Fractal Space-Time: Application to Quantum Physics, Cosmology and  Chaotic systems"
    Sec. 7.2.2
     
  • Nottale, L., Schumacher, G., Gay, J., 1997,  Astron. Astrophys., 322, 1018

    •  "Scale Relativity and Quantization of the Solar System". (PDF)
     
  • Nottale L. & Schumacher G., 1998, in "Fractals and beyond : Complexities in the Sciences", Proceedings of  'Fractal 98' conference, (World Scientific), Ed. M.M. Novak, p.

    • 149.  (PDF)
    "Scale relativity, fractal space-time and gravitational structures"
    Sec. 3.2
     
  • Nottale, L., 1998, Chaos, Solitons and Fractals, 9, 1035    (Abstract)   (PDF)

    •  "Scale relativity and quantization of planet obliquities"

    Extrasolar planets
     

  • Nottale L., 1996, Astron. Astrophys. Lett. 315, L9.   (PDF)

    • "Scale-Relativity and Quantization of Extrasolar Planetary Systems"
     
  • Nottale, L., 1998, Chaos, Solitons and Fractals, 9, 1043    (Abstract)

    •  "Scale Relativity and Quantization of the Planetary System around the pulsar PSR B1257+12"
     
  • Nottale L. & Schumacher G., 1998, in "Fractals and beyond : Complexities in the Sciences", Proceedings of  'Fractal 98' conference, (World Scientific), Ed. M.M. Novak, p. 149.  (PDF)

    • "Scale relativity, fractal space-time and gravitational structures"
    Sec. 3.2
     
  • Nottale L., Schumacher G., & Lefèvre E.T., 2000, Astron. Astrophys., 361, 379.   (PostScript) (PDF)

    • "Scale relativity and quantization of exoplanet orbital semi-major axes"
     
  • Nottale L., 2002, in Traité IC2, Traitement du Signal et de l'Image, "Lois d'échelle, fractales et ondelettes", sous la direction de P. Abry, P. Gonçalvès et J. Levy Vehel  (Hermès Lavoisier 2002), Vol. 2, Chap. 7, pp. 233-265. (PDF)

    •  "Relativité d'échelle, nondifférentiabilité et espace-temps fractal" (in French)
    Sec. 7.6.2
     
  • L. Nottale, P. Galopeau, D. Ceccolini, D. DaRocha,  G. Schumacher and N. Tran-Minh, 2003, Poster présenté au XIXè colloque IAP "Extrasolar Planets: Today and Tomorrow", 30 juin-4 Juillet 2003 (PDF) (JPEG)

    • "Structuring of the semi-major axis and eccentricity distributions of exoplanets"
     
  • P. Galopeau, L. Nottale, D. Ceccolini, D. DaRocha,  G. Schumacher and N. Tran-Minh, 2004, in "Scientific Highlights 2004", Proceedings of the Journées de la SF2A, Paris 14-18 Juin 2004, F. Combes, D. Barret, T. Contini, F. Meynadier & L. Pagani (eds.), EDP Sciences, p. 75 (Poster shown at the "Journées de la SF2A") (JPEG)(PDF)

    • "Distribution of orbital elements of planets and exoplanets in scale relativity"

    APPLICATIONS IN SCIENCES OF LIFE AND HUMAN SCIENCES

    Log-periodic evolutionary laws

    Species evolution
     

  • Chaline, J., Nottale, L., Grou, P., 1999, C.R. Acad. Sci. Paris, 328, IIa, 717  (PDF)

    •  "Is the evolutionary tree a fractal structure ?"
    Reprinted in: "Points sur... Sciences de la Terre IX: évolution", (Académie des Sciences, Elsevier 2001)
     
  • Nottale L., 2001, Revue de Synthèse, T. 122, 4e S., N°1, janvier-mars 2001, p. 93-116 (PDF)

    • "Relativité d'échelle et morphogenèse" (en français)
    Sec. 3.1.2
     
  • Nottale, L., Chaline, J., & Grou, P., 2001, in "Fractals in Biology and Medicine", Vol III, Proceedings of Fractal 2000 Third International Symposium, Eds. G. Losa, D. Merlini, T. Nonnenmacher and E. Weibel, Birckhäuser Verlag, p. 247.

    •  "On the fractal structure of evolutionary trees"     (PDF)
    Sec. 3.3
     
  • Nottale L., 2004, contribution invitée à CASYS'03, Sixth International Conference  on Computing Anticipatory Systems (Liège, Belgique, Aout 2003), à l'occasion de la remise du CASYS Award. AIP Conference proceedings, à paraître  (PDF)

    • "The Theory of Scale Relativity: Non-Differentiable Geometry and Fractal Space-Time"
    Sec. 6.4.2

    Evolution of societies
     

  • Nottale L., 2001, Revue de Synthèse, T. 122, 4e S., N°1, janvier-mars 2001, p. 93-116 (PDF)

    • "Relativité d'échelle et morphogenèse" (in French)
    Sec. 3.1.2
     
  • Nottale, L., Chaline, J., & Grou, P., 2001, in "Fractals in Biology and Medicine", Vol III, Proceedings of Fractal 2000 Third International Symposium, Eds. G. Losa, D. Merlini, T. Nonnenmacher and E. Weibel, Birckhäuser Verlag, p. 247.

    •  "On the fractal structure of evolutionary trees"     (PDF)
    Sec. 3.4
     
  • Grou P., Nottale L.,Chaline J., 2002, présenté dans  "Evénements rapides, instabilités, changements culturels au quaternaire", Colloquium, Aix-en-Provence. Publié dans "En mémoire de E. Aguirre", sous presse  (PDF)

    •  "Evolution morphologique et culturelle humaine: l'apport des modèles fractals" (in French)

    Human development
     

  • Cash R., Chaline, J., Nottale, L., Grou, P., 2002, C.R. Biologies  325, 585-590   (PDF)

    •  "Human development and log-periodic law".

    Morphogenesis
     

  • Nottale, L., 2000, Conférence invitée, Proceedings of 4è Forum Halieumétrique, Juin 1999, Les espaces de l'halieutique, Eds. D. Gascuel, P. Chavance, N. Bez & A. Biseau, IRD Editions, p.41  (PDF)

    •  "La théorie de la relativité d'échelle: réflexions pour une application à l'halieutique" (in French)
     
  • Nottale L., 2001, Revue de Synthèse, T. 122, 4e S., N°1, janvier-mars 2001, p. 93-116 (PDF)

    • "Relativité d'échelle et morphogenèse" (in French)
     
  • Nottale L., 2004, invited contribution in CASYS'03, Sixth International Conference  on Computing Anticipatory Systems (Liège, Belgium, August 2003). To appear in: AIP Conference Proceedings (PDF)

    • "The Theory of Scale Relativity: Non-Differentiable Geometry and Fractal Space-Time"
    Sec. 4.2.1

    Formation, duplication, bifurcation
     

  • Nottale L., 2004, invited contribution in CASYS'03, Sixth International Conference  on Computing Anticipatory Systems (Liège, Belgium, August 2003). To appear in: AIP Conference Proceedings (PDF)

    • "The Theory of Scale Relativity: Non-Differentiable Geometry and Fractal Space-Time"
    Sec. 4.2.2

    Hierarchy of organisation
     

  • Nottale L., 2004, invited contribution in CASYS'03, Sixth International Conference  on Computing Anticipatory Systems (Liège, Belgium, August 2003). To appear in: AIP Conference Proceedings (PDF)

    • "The Theory of Scale Relativity: Non-Differentiable Geometry and Fractal Space-Time"
    Sec. 6