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Argyris, J.; Ciubotariu, C.; Matuttis, H.-G.

Fractal space, cosmic strings and spontaneous symmetry breaking. (English) Zbl 1040.83520

Chaos Solitons Fractals 12, No. 1, 1-48 (2001).

Cited in 16 Documents

MSC:

83E30 String and superstring theories in gravitational theory
37F35 Conformal densities and Hausdorff dimension for holomorphic dynamical systems
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[1] El Naschie, M. S., Dimensional symmetry breaking, information and fractal gravity in Cantorian space, BioSystems, 46, 41-46 (1998)
[2] Omohundro, S. M., Geometric perturbation theory in physics (1986), World Scientific: World Scientific Singapore · Zbl 0830.58036
[3] Grandy WT Jr., Foundation of statistical mechanics, vol. I: Equilibrium theory. Dordrecht: D. Reidel, 1987; Grandy WT Jr., Foundation of statistical mechanics, vol. I: Equilibrium theory. Dordrecht: D. Reidel, 1987 · Zbl 0721.60119
[4] Rueda, A.; Cavalleri, G., Zitterbewegung in stochastic electrodynamics and implications on a zero-point field acceleration mechanism, Nuovo Cimento, 6C, 3, 239-260 (1983)
[5] Peebles, P. J.E., Principles of physical cosmology (1993), Princeton University Press: Princeton University Press Princeton, NJ · Zbl 1002.83527
[6] El Naschie, M. S., On the 26-dimensional Leech lattice and \(E^∞\), Chaos, Solitons & Fractals, 10, 11, 1813-1819 (1999) · Zbl 1035.81509
[7] DelaPeña, L.; Cetto, A. M., Quantum phenomena and the zeropoint radiation field, Found Phys, 24, 6, 917-925 (1994)
[8] Felegara, A., The relevance of the Algebraic approach to the quantum field theory in curved backgrounds, Fortschr Phys, 7, 1-2, 117-123 (1989)
[9] Semiz, I., Black hole as the ultimate energy source, Am J Phys, 63, 2, 151-156 (1995)
[10] Argyris, J.; Ciubotariu, C., Complexity in spacetime and gravitation I. From chaos to superchaos, Chaos, Solitons & Fractals, 9, 10, 1651-1701 (1998) · Zbl 0989.37023
[11] Leinaas, J., Hawking radiation, the Unruh effect and the polarisation of electrons, Europhys News, 2, 4, 78-80 (1991)
[12] Matsas, G. E.A., Do inertial electric charges radiate with respect to uniformly accelerated observers, Gen Rel Grav, 26, 11, 1165-1169 (1994)
[13] Leader, E.; Predazzi, E., An introduction to gauge theories and the new physics (1982), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1139.81300
[14] Kibble T. Of particles, pencils, and unification. Preprint 1993, Department of Physics, Imperial College, London, UK; Kibble T. Of particles, pencils, and unification. Preprint 1993, Department of Physics, Imperial College, London, UK
[15] Mahajan SM. Field, Particles and Universe. Lecture Notes, Spring College on Plasma Physics, 17 May - 11 June 1993, H4-SMR 692/29, Preprint ICTP, Trieste; Mahajan SM. Field, Particles and Universe. Lecture Notes, Spring College on Plasma Physics, 17 May - 11 June 1993, H4-SMR 692/29, Preprint ICTP, Trieste
[16] Hands S. Ripples at the heart of physics. Preprint 1993, Theory Division, CERN, Geneva, Switzerland; Hands S. Ripples at the heart of physics. Preprint 1993, Theory Division, CERN, Geneva, Switzerland
[17] Copeland, E. J., Cosmic strings. A particle physics solution to the large-scale structure of the Universe, CERN Courier, 31, 6, 17-19 (1991)
[18] Martin, J. L., General relativity: a guide to its consequences for gravity and cosmology (1988), Ellis Horwood Limited: Ellis Horwood Limited Chichester
[19] Chang, T., Maxwells equations in anisotropic space, Phys Lett, 70A, 1, 1-2 (1979)
[20] Piran T. On fravitational repulsion. Gen Rel Grav 1997;29:1363-70 (e-print http://xxx.lanl.gov/abs/gr-qc/9706049; Piran T. On fravitational repulsion. Gen Rel Grav 1997;29:1363-70 (e-print http://xxx.lanl.gov/abs/gr-qc/9706049 · Zbl 0892.53045
[21] Hagai, El-Ad, Piran T. Voids in the large-scale structure. Astrophys J 1997; 491: 421-39 (e-print archive, http://xxx.lanl.gov/abs/astro-ph/9702135; Hagai, El-Ad, Piran T. Voids in the large-scale structure. Astrophys J 1997; 491: 421-39 (e-print archive, http://xxx.lanl.gov/abs/astro-ph/9702135
[22] Piran T, Lecar M, Goldwirth DS, NicolacidaCosta L, Blumenthal GR. Limits on the primordial fluctuation spectrum void sizes and CMBR anisotropy, e-print archive http://xxx.lanl.gov/abs/astro-ph/9305019; Piran T, Lecar M, Goldwirth DS, NicolacidaCosta L, Blumenthal GR. Limits on the primordial fluctuation spectrum void sizes and CMBR anisotropy, e-print archive http://xxx.lanl.gov/abs/astro-ph/9305019
[23] Rosen, G., Black holes associated with galaxies, Int J Theor Phys, 30, 11, 1517-1520 (1991)
[24] Vilenkin A. Cosmic strings and other topological defects, In: Humitaka S, Takeo I, editors. Quantum gravity and cosmology. Singapore: World Scientific, 1985: 269-300; Vilenkin A. Cosmic strings and other topological defects, In: Humitaka S, Takeo I, editors. Quantum gravity and cosmology. Singapore: World Scientific, 1985: 269-300
[25] Witten, E., Superconducting strings, Nucl Phys B, 249, 557-569 (1985)
[26] Linet, B., Electro-gravitational conversion in the spacetime of an infinite straight superconducting cosmic string, Phys Lett, 146A, 4, 159-161 (1990)
[27] Carter B, Peter P, Gangui A, Avoidance of collapse by circular current-carrying cosmic string loops. Phys Rev D 1996;54:4647-62 (e-print archive, http://xxx.lanl.gov/abs/hep-ph/9609401; Carter B, Peter P, Gangui A, Avoidance of collapse by circular current-carrying cosmic string loops. Phys Rev D 1996;54:4647-62 (e-print archive, http://xxx.lanl.gov/abs/hep-ph/9609401
[28] Brandenberger R, Carter B, Davis A-C, Trodden M. Cosmic vortons and particle physics constraints. Phys Rev D 1997;55:6059-71 (e-print archive, http://xxx.lanl.gov/abs/hep-ph/9605382; Brandenberger R, Carter B, Davis A-C, Trodden M. Cosmic vortons and particle physics constraints. Phys Rev D 1997;55:6059-71 (e-print archive, http://xxx.lanl.gov/abs/hep-ph/9605382
[29] Martínez, V. J., Is the universe fractal?, Science, 284, 445-446 (1999)
[30] Peebles, P. J.E., The fractal galaxy distribution, Physica D, 38, 273-278 (1989)
[31] Luo, X.; Schramm, D. N., Fractals and cosmological large-scale structure, Science, 256, 513-515 (1992)
[32] El Naschie, M. S., Time symmetry breaking, duality and Cantorian space-time, Chaos, Solitons & Fractals, 7, 4, 499-518 (1996) · Zbl 1080.81514
[33] Argyris, J.; Ciubotariu, C.; Weingaertner, W. E., Progress in physical concepts of string and superstring theory - Thirty years of string theory, Chaos, Solitons & Fractals, 10, 2-3, 225-256 (1999) · Zbl 0997.81099
[34] DerSarkissian, M., Possible evidence for gravitational Bohr orbits in double galaxies, Lettere al Nuovo Cimento, 44, 8, 629-636 (1985)
[35] Isham C. Quantum gravity. In: Davies P, editor. The new physics, Cambridge: Cambridge University Press, 1992; Isham C. Quantum gravity. In: Davies P, editor. The new physics, Cambridge: Cambridge University Press, 1992
[36] Ball, R. C.; Witten, T. A., Causality bound on the density of aggregates, Phys Rev A, 29, 5, 2966-2967 (1984)
[37] Ord, G. N., Fractal space-time and the statistical mechanics of random walks, Chaos, Solitons & Fractals, 7, 6, 821-843 (1996) · Zbl 1080.82542
[38] Mandelbrot, B. B., The fractal geometry of nature (1983), Freeman: Freeman New York · Zbl 0504.28001
[39] Kolb, E.; Turner, M. S., The early universe (1989), Addison-Wesley: Addison-Wesley San Francisco
[40] Argyris J, Rössler OE. Distance-proportional redshift in \(1+ε\); Argyris J, Rössler OE. Distance-proportional redshift in \(1+ε\)
[41] DeSabbata, V.; Sivaram, C., Fifth force as a manifestation of torsion, Int J Theor Phys, 29, 1, 1-6 (1990) · Zbl 0694.53064
[42] Corinaldesi, E.; Strocchi, F., Relativistic wave mechanics (1963), North-Holland: North-Holland Amsterdam · Zbl 0114.20203
[43] Nelson, E., Derivation of the Schrödinger equation from Newtonian mechanics, Phys Rev, 150, 1079-1085 (1966)
[44] Reuter M. Gravitational anyonisation. Preprint DESY 91-007, ITP-UH 1/91, Institute of Theoretical Physics, University of Hannover, February 1991; Reuter M. Gravitational anyonisation. Preprint DESY 91-007, ITP-UH 1/91, Institute of Theoretical Physics, University of Hannover, February 1991
[45] Gasperini, M., Broken Lorentz symmetry and the dimension of space-time, Phys Lett B, 180, 3, 221-224 (1986)
[46] El Naschie, M. S., Dimensional symmetry breaking and gravity in Cantorian space, Chaos, Solitons & Fractals, 8, 5, 753-759 (1997) · Zbl 0936.83042
[47] Long, D. R., Vacuum polarisation and non-Newtonian gravitation, Nuovo Cimento, 55B, 2, 252-256 (1980)
[48] El Naschie, M. S., A note on quantum gravity and Cantorian spacetime, Chaos Solitons & Fractals, 8, 1, 131-133 (1997) · Zbl 0945.83004
[49] Vilenkin, A., Cosmic strings and domain walls, Phys Rep, 121, 5, 263-315 (1985) · Zbl 0966.83541
[50] Sornborger A. The structure of cosmic string wakes. PhD Thesis, Department of Physics, Brown University, 1996; Sornborger A. The structure of cosmic string wakes. PhD Thesis, Department of Physics, Brown University, 1996
[51] Eddington, A. S., The Mathematical Theory of Relativity (1924), Cambridge University Press: Cambridge University Press Cambridge · JFM 50.0605.01
[52] Luminet, J.-P.; Starkman, G. D.; Weeks, J. R., Is space finite?, Scientific American, 280, 4, 68-75 (1999)
[53] Lachièze-Rey M, Luminet J-P. Cosmic topology. Phys Rep 1995;254(3):135-214 (xxx.lanl.gov/abs/gr-qc/9605010); Lachièze-Rey M, Luminet J-P. Cosmic topology. Phys Rep 1995;254(3):135-214 (xxx.lanl.gov/abs/gr-qc/9605010)
[54] Bak D, Kim SP, Kim SK, Soh K-S, Yee JH. Fractal diffraction grating, Preprint available at http://xxx.lanl.gov/abs/physics/9802007; Bak D, Kim SP, Kim SK, Soh K-S, Yee JH. Fractal diffraction grating, Preprint available at http://xxx.lanl.gov/abs/physics/9802007
[55] Nottale L. Scale relativity, fractal space-time and quantum mechanics. Chaos, Solitons & Fractals 1994;4:361-88. Reprinted in: El Naschie MS, Rössler OE, Prigogine I. Quantum mechanics, diffusion and chaotic fractals. Oxford: Elsevier, 1995: 51-78; Nottale L. Scale relativity, fractal space-time and quantum mechanics. Chaos, Solitons & Fractals 1994;4:361-88. Reprinted in: El Naschie MS, Rössler OE, Prigogine I. Quantum mechanics, diffusion and chaotic fractals. Oxford: Elsevier, 1995: 51-78
[56] Uozumi, J.; Peiponen, K.-E.; Savolainen, M.; Silvennoinen, R.; Asakura, T., Demonstration of diffraction by fractals, Am J Phys, 62, 3, 283-285 (1994)
[57] Nelson, E., Quantum fluctuations (1985), Princeton University Press: Princeton University Press Princeton, NJ · Zbl 0563.60001
[58] Ord, G. N., Fractal space-time: a geometric analogue of relativistic quantum mechanics, J Phys A: Math Gen, 16, 1869-1884 (1983)
[59] Collins, P. D.B.; Martin, A. D.; Squires, E. J., Particle physics and cosmology (1989), Wiley: Wiley New York
[60] Sterman, G., Quantum field theory (1993), Cambridge University Press: Cambridge University Press Cambridge
[61] Davies P. Superforce. London: Unwin Hyman Ltd, 1987; Davies P. Superforce. London: Unwin Hyman Ltd, 1987
[62] El Naschie, M. S., Stress, stability and chaos in structural engineering: an energy approach (1990), McGraw-Hill: McGraw-Hill London
[63] Nicolis G. Physics of far-from-equilibrium systems and self-organisation. In: Davies P, editor. The new physics, Cambridge: Cambridge University Press, 1992; Nicolis G. Physics of far-from-equilibrium systems and self-organisation. In: Davies P, editor. The new physics, Cambridge: Cambridge University Press, 1992
[64] Peat FD. Superstrings and the search for the theory of everything. contemporary Books, 1988; Peat FD. Superstrings and the search for the theory of everything. contemporary Books, 1988
[65] Rae IM. Quantum mechanics. 3rd ed. Bristol: Institute of Physics Publishing, 1993; Rae IM. Quantum mechanics. 3rd ed. Bristol: Institute of Physics Publishing, 1993
[66] Lawrie ID. A unified grand tour of theoretical physics. 3rd ed. Bristol: Institute of Physics Publishing, 1990; Lawrie ID. A unified grand tour of theoretical physics. 3rd ed. Bristol: Institute of Physics Publishing, 1990 · Zbl 0743.53044
[67] Argyris, J.; Ciubotariu, C., A metric for an Evans-Vigier field, Found Phys Lett, 11, 2, 141-163 (1998)
[68] Bohm, D.; Aharonov, Y., Significance of electromagnetic potentials in the quantum theory, Phys Rev, 115, 485-491 (1959) · Zbl 0099.43102
[69] Bohm, D.; Aharonov, Y., Further considerations on electromagnetic potentials in the quantum theory, Phys Rev, 123, 1511-1524 (1961) · Zbl 0104.22205
[70] Peshkin, M.; Tonomura, A., The Aharonov-Bohm effect (1989), Springer: Springer New York
[71] Holstein, B. R., Variations on the Aharonov-Bohm effect, Am J Phys, 59, 12, 1080-1085 (1991)
[72] Felsager, B., Geometry, Particles and fields (1981), Odense Uniersity Press: Odense Uniersity Press Odense · Zbl 0489.58001
[73] Feynman, R. P.; Hibbs, A. R., Quantum mechanics and path integrals (1965), McGraw-Hill: McGraw-Hill New York · Zbl 0176.54902
[74] Möllenstedt, G.; Bayh, W., The continuous variation of the phase of electron waves in field free space by means of the magnetic vector potential of a solenoid, Phys Blätt, 18, 299-310 (1962)
[75] Tonomura, A.; Matsuda, T.; Suzuki, R.; Fukuhara, A.; Osakabe, N.; Umezaki, H.; Endo, J.; Shinagawa, K.; Sugita, Y.; Fujiwara, H., Observation of Aharonov-Bohm effect by electron holography, Phys Rev Lett, 48, 1443-1446 (1982)
[76] Gamboa, J.; Rivelles, V. O., Quantum mechanics of relativistic particles in multiply connected spaces and the Aharonov-Bohm effect, J Phys A, 24, L659-L666 (1991)
[77] Aharonov, Y.; Casher, A., Topological quantum effects for neutral particles, Phys Rev Lett, 53, 319-321 (1984)
[78] Cimmins, A.; Cimmino, A.; Opat, G. I.; Klein, A. G.; Kaiser, H.; Werner, S. A.; Arif, M.; Clothier, R., Observation on the topological Aharonov-Casher phase shift by neutron interferometry, Phys Rev Lett, 63, 380-383 (1989)
[79] London F. Superfluids. vol. I. New York: Wiley, 1950; London F. Superfluids. vol. I. New York: Wiley, 1950 · Zbl 0041.58507
[80] Argyris, J.; Ciubotariu, C., A nonlinear chaotic gravitational-wave detector, Chaos, Solitons & Fractals, 10, 1, 51-76 (1999) · Zbl 0973.83506
[81] Semon, M. D., Experimental verification of an Aharonov-Bohm effect in rotating reference frames, Found Phys, 12, 49-57 (1982)
[82] Zimmerman, J. E.; Mercereau, J. E., Compton wavelength of superconducting electrons, Phys Rev Lett, 14, 887-888 (1965)
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