List of papers downloadable from this site, by inverse chronological order. (By topic, see here)

Updated: November 4, 2011 

Nottale L. & Lehner Th., 2012, Int. J. Mod. Phys. C23 (5), 1250035 (27 pages)
``Numerical simulation of a macro-quantum experiment: oscillating wave packet"

L. Nottale, 2011, arXiv:gr-qc/0307042v2 (revised version)
"The Pioneer anomalous acceleration: can we measure the cosmological constant at the scale of the solar system ?"

Célérier M.-N. & Nottale L., 2010, Int. J. Mod. Phys. A25, 4239-4253  (arXiv:1009.2934)
"Electromagnetic Klein-Gordon and Dirac equations in scale relativity"

Nottale L., 2010, in Proceedings of First International Conference on the Evolution and Development of the Universe, 8 - 9 October 2008, ENS, Paris, France, Foundations of Science, 15, 101-152 (arXiv:0812.3857)
"Scale relativity and fractal space-time: theory and applications"

Nottale L., 2009,  (arXiv:0901.1270)
"Quantum-like gravity waves and vortices in a classical fluid"

Nottale L., 2009, J. Phys. A: Math. Theor. 42, 275306 (arXiv:0812.0941)
" Generalized quantum potentials "

Nottale L., 2008, in "Workshop Pulsars, Théories et Observations", 24-26 Novembre 2008, Observatoire de Paris.
"Formation et évolution du système planétaire de PSR B1257+12" (in French)

Auffray C. & Nottale L., 2008, Progress in Biophysics and Molecular Biology, 97, 79-114 
    "Scale relativity theory and integrative systems biology. 1. Founding principles and scale laws"

Nottale L. & Auffray C., 2008, Progress in Biophysics and Molecular Biology, 97, 115-157 
    "Scale relativity theory and integrative systems biology. 2. Macroscopic quantum-type mechanics"

Nottale L., 2007, in "La mesure en physique", LUTH workshop, 23 November 2007 
"Relativité d’échelle de la mesure" (in French)

Nottale L.& Célérier M.N., 2007, J. Phys. A: Math. Theor. 40, 14471-14498  (arXiv:0711.2418) [quant-ph]
"Derivation of the postulates of quantum mechanics from the first principles of scale relativity" 

Nottale L., 2007, in Les grands défis technologiques et scientifiques au XXIe siècle, under the direction of Philippe Bourgeois et Pierre Grou (Ellipses).  
"Un nouveau paradigme pour la physique ? Nouvelles perspectives"  (in French)

  • Nottale L., 2007, Invited contribution in the Special Issue of the Electronic Journal of Theoretical Physics  on "Physics of Emergence and Organization", EJTP 4, No 16(II), 187-274   (Review Paper, 88 pp.)
    • "Scale Relativity: A Fractal Matrix for Organization in Nature".
     
  • Nottale L., 2007, Invited Conference, in Proceedings of International Colloquium "Albert Einstein and Hermann Weyl: 50th anniversary of their death, open epistemologic questions" (Lecce, Italy, 2005), in press
    • "Foundation of  gauge field theories on the principle of scale relativity".
     
  • Nottale L., 2007, New Advances in Physics, 1, 55 
    • "Foundation of quantum mechanics and gauge field theories in scale relativity".
     
  • Nottale L., 2007, Invited Conference  in "Frontiers of Fundamental Physics", Proceedings of the Eight International Symposium "Frontiers of Fundamental and Computational Physics", Madrid, Spain, 17-19 October 2006, Eds. Sidharth B.G. et al., A.I.P. Conf. Proc., 905, 188
    • "Foundation of quantum mechanics from the principle of relativity".
     
  • Célérier M.N. & Nottale L., 2006, J. Phys. A, 39, 12565  (arXiv:quant-ph/0609107)
    • "The Pauli equation in scale relativity"
     
    Nottale L. & Lehner T., 2006 (arXiv:quant-ph/0610201) 
    "Numerical simulation of a macroscopic quantum-like experiment: oscillating wave packet"

  • Nottale L., 2008, in « Proceedings of 7th International Colloquium on Clifford Algebra », Toulouse, France, 19-29 Mai 2005, Advances in Applied Clifford Algebra, 18, 917-944 
    • "Origin of complex and quaternionic wavefunctions in quantum mechanics: the scale-relativistic view".
     
  • Nottale L., Célérier M.N. & Lehner T., 2006,  J. Math. Phys. 47, 032303  (arXiv:hep-th/0605280) (Old version 2003: arXiv:hep-th/0307093)
    • "Non Abelian gauge field theory in scale relativity"
     
  • Nottale L. 2006, Invited Conference in "Frontiers of Fundamental Physics", Proceedings of the Sixth International Symposium "Frontiers of Fundamental and Computational Physics", Udine, Italy, 26-29 September 2004, Sidharth, B.G., Honsell, F. & de Angelis, A. (Eds.),  Springer, pp.107-114 
    •  "Astrophysical applications of the theory of scale relativity".
     
  • Auffray C., Nottale L. & the Systemoscope Consortium, 2005, Invited Conference in International Conference "Integrative Systems Biology for Health - TRANSCRIPTOME 2005", Shanghai, China, 5-9 November 2005 
    •  "Scale Relativity in Systems Biology of Muscular and Pulmonary Diseases"
     
  • L. Nottale, 2005, Progress in Physics, 1, 12-16
    • "Fractality field in the theory of scale relativity"
     
  • Nottale L., 2005, Chaos, Solitons and Fractals, 25, 797-803
    • "On the transition from the classical to the quantum regime in fractal space-time theory"
     
  • Contributions to the "Journées de la SF2A 2004":  published 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 (PDF)
    1. Nottale L., "Energy structure at 3.2 10^20 eV in special scale-relativity", p. 373
    2. Célérier M.N. & Nottale L., "Generalized macroscopic Schrödinger equation in scale relativity", p. 649  (arXiv:gr-qc/0505012)
    3. Lehner T., Nottale L., di Menza L., da Rocha D., & Ceccolini D., "Structure formation by the Hartree equation", p. 687
    4. Nottale L., "Scale relativity and dark potential", p. 699
    5. Galopeau P., Nottale L., Ceccolini D., da Rocha D., Schumacher G. & Tran-Minh N., "Distribution of orbital elements of planets and exoplanets in scale relativity", p. 75
  • 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")
    • "Distribution of orbital elements of planets and exoplanets in scale relativity"
     
  • Nottale L., 2004, invited contribution (reception of the CASYS'03 award), in "Computing Anticipatory Systems. CASYS'03 - Sixth International Conference" (Liège, Belgique, 11-16 August 2003), Daniel M. Dubois Editor, American Institute of Physics Conference Proceedings  718, 68-95
    • "The Theory of Scale Relativity: Non-Differentiable Geometry and Fractal Space-Time"
     
  • Célérier M.N. & Nottale L., 2004, J. Phys. A 37, 931-955
    • "Quantum-classical transition in scale relativity"
     
  • L. Nottale, D. Ceccolini, D. DaRocha,  N. Tran-Minh, P. Galopeau, G. Schumacher, 2003, in  "Extrasolar Planets: Today and Tomorrow", Proceedings of  IAP meeting, Paris, 30 juin-4 Juillet 2003, Eds. J.P. Beaulieu, A. Lecavelier des Etangs and C. Terquem, Astronomical  Society of the Pacific Conference Series vol. 321, p. 355  (JPEG)
    • "Structuring of the semi-major axis and eccentricity distributions of exoplanets"
     
  • Da Rocha D. & Nottale L., 2003,  unpublished preprint (PDF)  (arXiv:astro-ph/0310031)
    •  "On the morphogenesis of stellar flows. Application to planetary nebulae".
     
  • Nottale L., 2003, Invited Conference, first joint AMS/SMF meeting, ENS Lyon, 17-20 July 2001 (unpublished preprint) 
    • "Fractal Space-Time, Nondifferentiable Geometry and Scale Relativity"
     
  • Da Rocha D. & Nottale L., 2003, Chaos Solitons and Fractals, 16, 565 (arXiv:astro-ph/0310036)  (Review paper about applications to astrophysics)
    • "Gravitational structure formation in scale relativity"
     
  • Nottale L., 2003, Chaos Solitons and Fractals, 16, 539   (PDF) (Review of applications to cosmology)
    • "Scale-relativistic cosmology"
     
  • Nottale L., 2003, Electromagnetic Phenomena T. 3, N°1 (9), 24, special issue dedicated to the  75th anniversary of the discovery of the Dirac equation.  
    • "Theory of Electron in Scale Relativity"
     
  • 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"
     
  • Grou P., Nottale L.,Chaline J., 2002, presented in "Evénements rapides, instabilités, changements culturels au quaternaire", Colloquium, Aix-en-Provence. Published in volume "Zona Arqueologica, Miscelanea en homenaje a Emiliano Aguirre”, vol. IV Arqueologia : p. 230-237, Museo Arquelogico Regional, Madrid, 2004.
    •  "Log-periodic laws applied to geosciences "  (In French)
     
  • Nottale, L., 2002, in "Penser les limites. Ecrits en l'honneur d'André Green", sous la direction de César Botella, (Delachiaux et Niestlé, Paris, 2002), p. 157. 
    •  "Relativité, être et ne pas être" (in french)
     
  • Cash R., Chaline, J., Nottale, L., Grou, P., 2002, C.R. Biologies  325, 585-590
    •  "Développement humain et loi log-périodique".
     
  • Nottale L., 2002, invited conference in  International Colloquium "Géométrie au XXè siècle", Paris, 24-29 Septembre 2001 (unpublished preprint) 
    • "Non-differentiable space-time and 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. 
    •  "Relativité d'échelle, nondifférentiabilité et espace-temps fractal" (in french)
     
  • Célérier M.N. & Nottale L., 2001,  (arXiv:hep-th/0112213)
    • "Dirac equation in Scale relativity"
     
  • Nottale L., 2001, Chaos, Solitons and Fractals, 12, 1577
    •  "Scale relativity and gauge invariance".  (Abstract)
     
  • 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"  
     
  • Nottale L., 2001, Revue de Synthèse, T. 122, 4e S., N°1, janvier-mars 2001, p. 93-116 
    • "Relativité d'échelle et morphogenèse" (in french)
     
  • Nottale L., 2001, Revue de Synthèse, T. 122, 4e S., N°1, janvier-mars 2001, p. 11-25  (PDF)
    • "Relativité d'échelle: structure de la théorie" (in french)
     
  • Nottale L., 2001, invited conference in  Frontiers of Fundamental Physics, Proceedings of Birla Science Center Fourth International Symposium, 11-13 dec. 2000, Hyderabad, India, Eds. B.G. Sidharth and M.V. Altaisky, (Kluwer Academic), p. 65.  (PDF)
    • "Scale relativity and non-differentiable fractal space-time"
     
  • Nottale L., Schumacher G., & Lefèvre E.T., 2000, Astron. Astrophys., 361, 379.  (PDF)
    • "Scale relativity and quantization of exoplanet orbital semi-major axes"
     
  • Nottale, L., 2000, invited conference in  "Science of the Interface", Proceedings of International Colloquium in honor of Otto Rössler, ZKM Karlsruhe, 18-21 May 2000, Ed. H. Diebner et al. (Genista, Tubingen, 2001), p. 38.  (PDF)
    • "Scale relativity, fractal space-time and morphogenesis of structures"
     
  • Nottale, L., 2000, invited conference, 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., 1999, Chaos, Solitons and Fractals, 10, 459   (PDF)
    • "The Scale-Relativity Program".
     
  • 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., 1998, Ciel et Terre, Bulletin de la Société royale belge d'Astronomie, vol 114 (2), 63-71.  (PDF)
    • "Relativité d'échelle et cosmologie".
     
  • 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"
     
  • Nottale, L., 1998, Chaos, Solitons and Fractals, 9, 1035    (Abstract)   (PDF)
    • "Scale relativity and quantization of planet obliquities"
     
  • Nottale, L., 1998, Chaos, Solitons and Fractals, 9, 1043    (Abstract)  (PDF)
    • "Scale Relativity and Quantization of the Planetary System around the pulsar PSR B1257+12"
     
  • Nottale, L., 1998, Chaos, Solitons and Fractals, 9, 1051     (Abstract)  (PDF)
    • "Scale relativity and  Schrödinger's equation"
     
  • Nottale, L., Schumacher, G., Gay, J., 1997,  Astron. Astrophys., 322, 1018
    • "Scale Relativity and Quantization of the Solar System". (PDF)
     
  • Nottale L., 1997, Astron. Astrophys., 327, 867.   (PDF)
  • "Scale relativity and  Quantization of the Universe. I. Theoretical framework"
    •  
  • 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., 1996, Astron. Astrophys. Lett. 315, L9.   (PDF)
    • "Scale-Relativity and Quantization of Extrasolar Planetary Systems"
     
  • Nottale, L., 1996, Chaos, Solitons and Fractals, 7, 877-938    (PDF)
    • "Scale Relativity and Fractal Space-Time: Application to Quantum Physics, Cosmology and  Chaotic systems"
     
  • Nottale, L., 1995, in "Clustering in the Universe", 30th Rencontres de Moriond (Astrophysics meeting),  eds. S. Maurogordato, C. Balkowski, C. Tao and J. Tran Thanh Van (Frontières, 1995), pp. 523-529  (PDF)
  •  Nottale, L., 1995,   Chaos, Solitons & Fractals  6, 399.    (PDF)
    • "Scale-Relativity: From Quantum Mechanics to Chaotic Dynamics".
     
  • 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. 
    •  "New Formulation of Stochastic Mechanics. Application to Chaos".
     
  • Nottale, L., 1994, Chaos, Solitons & Fractals, 4, 361-388. 
    • 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".
     
  • 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. 
    •  "Scale-Relativity: First Steps toward a Field Theory".
     
  • Nottale, L., 1993, (World Scientific, 1993), 333 pp.
    • "Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity."
    Chapters 3.3: "Fractal Curves in a Plane", 3.4: "Non-Standard Analysis and Fractals", 3.5: "Fractal Curves in Space" and 3.6: "Fractal Surfaces", pp. 49-68 
     
  • Nottale, L., 1993, (World Scientific, 1993), 333 pp.
    • "Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity."
    Chapter 5.6: "Non-differentiable space and stochastic quantum mechanics", pp. 135-153  (complemented by notes and errata)
     
  • 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  (complemented by notes and errata)
     
  • Nottale, L., 1993, (World Scientific, 1993), 333 pp.
    • "Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity."
    Chapter 7.2: "Beyond Chaos", pp. 307-321 (complemented by notes and errata)
     
  • Nottale, L., 1992, Int. J. Mod. Phys. A7, 4899-4936  (complemented by notes and errata)
    • "The theory of scale relativity".

  • Nottale, L., Schneider, J., 1984, J. Math. Phys. 25, 1296-1300
    • "Fractals and Non-Standard Analysis".

    Unpublished preprints
     

  • Nottale L., 1993, preprint (PDF)

    • "Scale-relativistic Estimate of the Fine Structure Constant"
     
  • Nottale L., 1993, preprint (PDF)

    • "Scale-relativistic Estimate of the SU(3), SU(2) and U(1) Couplings"
     
  • Nottale L., 1993, preprint  (PDF)

    • "Mach's principle, Dirac's large numbers and the cosmological constant problem"


    Papers from other authors about scale-relativity (non exhaustive)
     
     
  • Hermann R., 1997, J. Phys. A: Math. Gen.30, 3967 (PDF)

    • "Numerical simulation of a quantum particle in a box"
     
  • Hermann R., Schumacher G., Guyard R., 1998, Astron. Astrophys. 335, 284   (PDF)

    • "Scale relativity and quantization of the solar system. Orbit quantization of the planet's satellites"
     
  • Pissondes, J.C., 1999, J. Phys. A: Math. Gen. 32, 2871   (PDF)

    • "Quadratic relativistic invariant and metric form in quantum mechanics"
     
  • Laperashvili L.V., Ryzhikh D.A., 2001,  arXiv:hep-th/0110127

    • "Phase transition in Gauge Theories and the Planck Scale Physics"
     
  • Cresson, J., 2003, J. Math. Phys.44, 4907

    • "Scale calculus and the Schrödinger equation"
     
  • da Rocha, D., 2004, PhD Thesis (Paris Observatory) (PDF)

    • "Gravitational structuring in scale relativity" (in French, abstract in English)
     
  • Cresson, J., 2006, International Journal of Geometric Methods in Modern Physics, Vol. 3, no. 7 (PDF)

    • "Non-differentiable deformations of Rn"
     
  • Jumarie, G., 2006, Chaos, Solitons and Fractals, sous presse (PDF)

    • "Lagrangian Mechanics of Fractional Order, Hamilton-Jacobi Fractional PDE and Taylor’s Series of Nondifferentiable Functions"