Beyond strings, multiple times and gauge theories of area-scalings relativistic transformations

Chaos, solitons and fractals

Volumn 10, Issue 2, 1999, Pages 295-309

  Castro, Carlos ^a  

^a CLARK ATLANTA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; FRACTALS; FUZZY SETS; GRAVITATION; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; RELATIVITY;

GAUGE INVARIANCE; LIE ALGEBRA; LORENTZ-SCALE RELATIVISTIC TRANSFORMATIONS; SCALE-MOTION RELATIVITY; SCALE-RELATIVITY PRINCIPLE; STRING THEORY;

QUANTUM THEORY;

EID: 0033075399     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(98)00090-3     Document Type: Article

References (57)

1. Tsetlyn, A., Int. Jour. Mod. Phys., 1989, A 4, 1257.
2. Nottale, L., Fractal spacetime and Microphysics: Towards the Theory of Scale Relativity. World Scientific, 1992; Int. Jour. Mod. Phys., 1989, A 4, 5047; 1992, A 7, 4899; Scale relativity, in Quantum Mechanics, Diffusion and Chaotic Fractals. Pergamon Press, Oxford, 1996, Vol. II; Scale relativity and quantization of the universe: theoretical framework, to appear in J. Astron. Astrophys.; Ord, G., J. Phys. A. Math. Gen., 1983, 16, 1869.
3. Nottale, L., Fractal spacetime and Microphysics: Towards the Theory of Scale Relativity. World Scientific, 1992; Int. Jour. Mod. Phys., 1989, A 4, 5047; 1992, A 7, 4899; Scale relativity, in Quantum Mechanics, Diffusion and Chaotic Fractals. Pergamon Press, Oxford, 1996, Vol. II; Scale relativity and quantization of the universe: theoretical framework, to appear in J. Astron. Astrophys.; Ord, G., J. Phys. A. Math. Gen., 1983, 16, 1869.
4. Nottale, L., Fractal spacetime and Microphysics: Towards the Theory of Scale Relativity. World Scientific, 1992; Int. Jour. Mod. Phys., 1989, A 4, 5047; 1992, A 7, 4899; Scale relativity, in Quantum Mechanics, Diffusion and Chaotic Fractals. Pergamon Press, Oxford, 1996, Vol. II; Scale relativity and quantization of the universe: theoretical framework, to appear in J. Astron. Astrophys.; Ord, G., J. Phys. A. Math. Gen., 1983, 16, 1869.
5. Nottale, L., Fractal spacetime and Microphysics: Towards the Theory of Scale Relativity. World Scientific, 1992; Int. Jour. Mod. Phys., 1989, A 4, 5047; 1992, A 7, 4899; Scale relativity, in Quantum Mechanics, Diffusion and Chaotic Fractals. Pergamon Press, Oxford, 1996, Vol. II; Scale relativity and quantization of the universe: theoretical framework, to appear in J. Astron. Astrophys.; Ord, G., J. Phys. A. Math. Gen., 1983, 16, 1869.
6. Nottale, L., Fractal spacetime and Microphysics: Towards the Theory of Scale Relativity. World Scientific, 1992; Int. Jour. Mod. Phys., 1989, A 4, 5047; 1992, A 7, 4899; Scale relativity, in Quantum Mechanics, Diffusion and Chaotic Fractals. Pergamon Press, Oxford, 1996, Vol. II; Scale relativity and quantization of the universe: theoretical framework, to appear in J. Astron. Astrophys.; Ord, G., J. Phys. A. Math. Gen., 1983, 16, 1869.
7. Nottale, L., Fractal spacetime and Microphysics: Towards the Theory of Scale Relativity. World Scientific, 1992; Int. Jour. Mod. Phys., 1989, A 4, 5047; 1992, A 7, 4899; Scale relativity, in Quantum Mechanics, Diffusion and Chaotic Fractals. Pergamon Press, Oxford, 1996, Vol. II; Scale relativity and quantization of the universe: theoretical framework, to appear in J. Astron. Astrophys.; Ord, G., J. Phys. A. Math. Gen., 1983, 16, 1869.
8. Castro, C., String theory, scale relativity and the generalized uncertainty principle, Found. Physics Lett., 1997, 10, 273.
9. Amati, D., Ciafaloni, M. and Veneziano, G. Phys. Lett., 1987, B 197, 81; Gross, D. and Mende, P., Phys. Lett., 1987, B 197, 129.
10. Amati, D., Ciafaloni, M. and Veneziano, G. Phys. Lett., 1987, B 197, 81; Gross, D. and Mende, P., Phys. Lett., 1987, B 197, 129.
11. Garay, L., Int. J. Mod. Phys., 1995, A 10, 145.
12. Ahtekar, A., Rovelli, C. and Smolin, L., Phys. Rev. Lett., 1992, 69, 237.
13. Ne'eman, Y.and Sijacki, D., Mod. Phys. Lett., 1996, A 11, 217.
14. Brandt, H., Finslerian spacetime, Contemporary Mathematics Series of The American Mathematical Society, 1996, 196, 273.
15. Aikou, T. and Ichijyo, Y., Rep. Fac. Science. Kagoshima Univ., 1990, 23, 101.
16. Ellis, J., Mavromatos, N. and Nanopoulos, D., Phys. Lett.,1992, B 293, 37; Mod. Phys. Lett., 1995, A 10, 425; Ellis, J., Mavromatos, N. and Nanopoulos, D., D Branes from Liouvilie strings, hep-th/9605046; Lizzi, F. and Mavromatos, N., Quantum phase space from string solitons, hep-th/9611040.
17. Ellis, J., Mavromatos, N. and Nanopoulos, D., Phys. Lett.,1992, B 293, 37; Mod. Phys. Lett., 1995, A 10, 425; Ellis, J., Mavromatos, N. and Nanopoulos, D., D Branes from Liouvilie strings, hep-th/9605046; Lizzi, F. and Mavromatos, N., Quantum phase space from string solitons, hep-th/9611040.
18. Ellis, J., Mavromatos, N. and Nanopoulos, D., Phys. Lett.,1992, B 293, 37; Mod. Phys. Lett., 1995, A 10, 425; Ellis, J., Mavromatos, N. and Nanopoulos, D., D Branes from Liouvilie strings, hep-th/9605046; Lizzi, F. and Mavromatos, N., Quantum phase space from string solitons, hep-th/9611040.
19. Ellis, J., Mavromatos, N. and Nanopoulos, D., Phys. Lett.,1992, B 293, 37; Mod. Phys. Lett., 1995, A 10, 425; Ellis, J., Mavromatos, N. and Nanopoulos, D., D Branes from Liouvilie strings, hep-th/9605046; Lizzi, F. and Mavromatos, N., Quantum phase space from string solitons, hep-th/9611040.
20. Bergshoeff, E., Sezgin, E., Tanni, Y. and Townsend, P., Annals of Phys., 1990, 199, 340; Guendelman, E., Nissiraov, E. and Pacheva, S., Volume-preserving diffeomorphisms versus local gauge symmetry, hep-th/9505128; Aurilia, A., Smailagic, A. and Spallucci, E., Phys. Rev., 1993,D 47, 2536; Castro, C., p-Branes as composite antisymmetric tensor field theories, Int. J. Mod. Physics A, 1998, 13, 1263.
21. Bergshoeff, E., Sezgin, E., Tanni, Y. and Townsend, P., Annals of Phys., 1990, 199, 340; Guendelman, E., Nissiraov, E. and Pacheva, S., Volume-preserving diffeomorphisms versus local gauge symmetry, hep-th/9505128; Aurilia, A., Smailagic, A. and Spallucci, E., Phys. Rev., 1993,D 47, 2536; Castro, C., p-Branes as composite antisymmetric tensor field theories, Int. J. Mod. Physics A, 1998, 13, 1263.
22. Bergshoeff, E., Sezgin, E., Tanni, Y. and Townsend, P., Annals of Phys., 1990, 199, 340; Guendelman, E., Nissiraov, E. and Pacheva, S., Volume-preserving diffeomorphisms versus local gauge symmetry, hep-th/9505128; Aurilia, A., Smailagic, A. and Spallucci, E., Phys. Rev., 1993,D 47, 2536; Castro, C., p-Branes as composite antisymmetric tensor field theories, Int. J. Mod. Physics A, 1998, 13, 1263.
23. Bergshoeff, E., Sezgin, E., Tanni, Y. and Townsend, P., Annals of Phys., 1990, 199, 340; Guendelman, E., Nissiraov, E. and Pacheva, S., Volume-preserving diffeomorphisms versus local gauge symmetry, hep-th/9505128; Aurilia, A., Smailagic, A. and Spallucci, E., Phys. Rev., 1993,D 47, 2536; Castro, C., p-Branes as composite antisymmetric tensor field theories, Int. J. Mod. Physics A, 1998, 13, 1263.
24. Duff, M., Class. Quant. Gravity, 1989, 6, 1577.
25. Ansoldi, S., Aurilia, A. and Spallucci, E., Hausdorff dimension of the quantum string, hep-th/9705010.
26. Kempf, A. and Mangano, G., Minimal length uncertainty and ultraviolet regularisation, hep-th/9612084; Mangano, G., Path integrals in noncommutative spaces, gr-qc/9705040.
27. Kempf, A. and Mangano, G., Minimal length uncertainty and ultraviolet regularisation, hep-th/9612084; Mangano, G., Path integrals in noncommutative spaces, gr-qc/9705040.
28. Thiemann, T., QSD V: Quantum gravity as a natural regulator of matter QFT, gr-qc/9705019.
29. Smolin, L., The future of spin networks, gr-qc/9702030.
30. Nowotny, T. and Requard, M., Dimension theory of graphs and networks, hep-th/9707082.
31. Datta, D., Duality and scalings in quantum mechanics, hep-th/9707055.
32. Madore, J., Classical gravity in fuzzy spacetime, gr-qc/9611026.
33. Pavsic, M., The Dirac-Nambu-Goto p-branes as particular solutions to a generalized unconstrained theory, IJS-TP-96-10 preprint.
34. Ansoldi, S., Aurilia, A. and Spallucci, E., String propagator, a loop space representation, hep-th/9510133.
35. Cederwall, M., Ferreti, G., Nilsson, B. and Westerby, A., Nucl. Phys., 1994, B 424, 97.
36. Yoneya, T., D-particles, D-instantons, and a spacetime uncertainty principle in string theory, hep-th/9707002.
37. Noyes, H., An Introduction to Bit String Physics, hep-th/9707020; Thorn, C., Supersymmetric Quantum Mechanics for String Bits, hep-th/9707048.
38. Noyes, H., An Introduction to Bit String Physics, hep-th/9707020; Thorn, C., Supersymmetric Quantum Mechanics for String Bits, hep-th/9707048.
39. Amelino-Camelia, G., Lukiersky, J. and Nowicki, A., κ deformed covariant phase space and quantum gravity uncertainty relations, hep-th/9706031.
40. Witten, E., Nucl. Phys., 1996, B 460, 333; Polchinski, J., Tasi Lectures on D-branes, hep-th/9611050; Banks, T., Fischler, W., Shenker, S. and Susskind, L., M theory as a Matrix model, a conjecture, hep-th/9610043; Hoppe, J., Quantum Theory of a Relativistic Surface, MIT, Ph.D thesis, 1980; Flume, R., Ann. Phys., 1985, 164, 189; Baake, M., Reinicke, P. and Rittenberg, V., J. Math. Phys., 1985, 265, 1070.
41. Witten, E., Nucl. Phys., 1996, B 460, 333; Polchinski, J., Tasi Lectures on D-branes, hep-th/9611050; Banks, T., Fischler, W., Shenker, S. and Susskind, L., M theory as a Matrix model, a conjecture, hep-th/9610043; Hoppe, J., Quantum Theory of a Relativistic Surface, MIT, Ph.D thesis, 1980; Flume, R., Ann. Phys., 1985, 164, 189; Baake, M., Reinicke, P. and Rittenberg, V., J. Math. Phys., 1985, 265, 1070.
42. Witten, E., Nucl. Phys., 1996, B 460, 333; Polchinski, J., Tasi Lectures on D-branes, hep-th/9611050; Banks, T., Fischler, W., Shenker, S. and Susskind, L., M theory as a Matrix model, a conjecture, hep-th/9610043; Hoppe, J., Quantum Theory of a Relativistic Surface, MIT, Ph.D thesis, 1980; Flume, R., Ann. Phys., 1985, 164, 189; Baake, M., Reinicke, P. and Rittenberg, V., J. Math. Phys., 1985, 265, 1070.
43. Witten, E., Nucl. Phys., 1996, B 460, 333; Polchinski, J., Tasi Lectures on D-branes, hep-th/9611050; Banks, T., Fischler, W., Shenker, S. and Susskind, L., M theory as a Matrix model, a conjecture, hep-th/9610043; Hoppe, J., Quantum Theory of a Relativistic Surface, MIT, Ph.D thesis, 1980; Flume, R., Ann. Phys., 1985, 164, 189; Baake, M., Reinicke, P. and Rittenberg, V., J. Math. Phys., 1985, 265, 1070.
44. Witten, E., Nucl. Phys., 1996, B 460, 333; Polchinski, J., Tasi Lectures on D-branes, hep-th/9611050; Banks, T., Fischler, W., Shenker, S. and Susskind, L., M theory as a Matrix model, a conjecture, hep-th/9610043; Hoppe, J., Quantum Theory of a Relativistic Surface, MIT, Ph.D thesis, 1980; Flume, R., Ann. Phys., 1985, 164, 189; Baake, M., Reinicke, P. and Rittenberg, V., J. Math. Phys., 1985, 265, 1070.
45. Witten, E., Nucl. Phys., 1996, B 460, 333; Polchinski, J., Tasi Lectures on D-branes, hep-th/9611050; Banks, T., Fischler, W., Shenker, S. and Susskind, L., M theory as a Matrix model, a conjecture, hep-th/9610043; Hoppe, J., Quantum Theory of a Relativistic Surface, MIT, Ph.D thesis, 1980; Flume, R., Ann. Phys., 1985, 164, 189; Baake, M., Reinicke, P. and Rittenberg, V., J. Math. Phys., 1985, 265, 1070.
46. Connes, A., Non Commutative Geometry. Academic Press, New York, 1994.
47. Vladimorov, V., Volovich, I. and Zelenov, E., p-Adic Analysis and Mathematical Physics. World Scientific, Singapore, 1992.
48. Castro, C., A Moyal Quantization of the Continuous Toda Field, Phys. Lett. B., 1997, 413, 53; Chapline, G. and Yamagishi, K., Class. Quant. Grav., 1991, 8, 427;
49. Castro, C., A Moyal Quantization of the Continuous Toda Field, Phys. Lett. B., 1997, 413, 53; Chapline, G. and Yamagishi, K., Class. Quant. Grav., 1991, 8, 427;
50. Nissimov, E. and Pacheva, S., Theor. Math. Phys., 1992, 93.
51. Bars, I., A case for 14 dimensions, hep-th/9704054.
52. Vafa, C., Evidence for F Theory, hep-th/9602022.
53. Fairlie, D., Goaverts, J. and Morozov, A., Nucl. Phys., 1992, B 373, 214.
54. Greene, B., String Theory on Calabi Yau Manifolds, hep-th/9702155; Aspinwall, P., K3 Surfaces and String Duality, hep-th/9611137.
55. Greene, B., String Theory on Calabi Yau Manifolds, hep-th/9702155; Aspinwall, P., K3 Surfaces and String Duality, hep-th/9611137.
56. El Naschie, M., Nottale, L., Al Athel, S. and Ord, G., Fractal spacetime and Cantorian Geometry in Quantum Mechanics, special issue of Chaos, Solitons and Fractals, 1996, 7 (6); El Naschie, M., Conrad, M., Rossler, O. and Ord, G., Nonlinear Dynamics, General Relativity and the Quantum, special issue of Chaos, Solitons and Fractals, 1997, 8 (5).
57. El Naschie, M., Nottale, L., Al Athel, S. and Ord, G., Fractal spacetime and Cantorian Geometry in Quantum Mechanics, special issue of Chaos, Solitons and Fractals, 1996, 7 (6); El Naschie, M., Conrad, M., Rossler, O. and Ord, G., Nonlinear Dynamics, General Relativity and the Quantum, special issue of Chaos, Solitons and Fractals, 1997, 8 (5).