Fractals and the fock-bargmann representation of coherent states

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5494, Issue , 2009, Pages 6-16

  Vitiello, Giuseppe ^a  

^a UNIVERSITY OF SALERNO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL FUNCTIONS; COHERENT STATE; DYNAMICAL FORMATION; FOCK-BARGMANN REPRESENTATION; GEOMETRICAL PROPERTY; LOCAL DEFORMATIONS; SELF SIMILARITY PROPERTIES;

COHERENT LIGHT;

FRACTALS;

EID: 67049098730     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-00834-4_3     Document Type: Conference Paper

References (26)

1. Bunde, A., Havlin, S. (eds.): Fractals in Science. Springer, Berlin (1995)
2. Peitgen, H.O., Jurgens, H., Saupe, D.: Chaos and fractals. New Frontiers of Science. Springer, Berlin (1986)
3. Vitiello, G.: Topological defects, fractals and the structure of quantum field theory. In: Licata, I., Sakaji, A. (eds.) The Nature Description in Quantum Field Theory. Open Problems and Epistemological Perspective. Springer, Berlin (in print, 2009)
4. Vitiello, G.: Coherent states, fractals and brain waves. New Mathematics and Natural Computation 5 (in print, 2009); Vitiello, G.: Self-similarity in fractals and coherent states (in preparation, 2009)
5. Vitiello, G.: Classical chaotic trajectories in quantum field theory. Int. J. Mod. Phys. B18, 785 (2004)
6. Bak, P., Creutz, M.: Fractals and self-organized criticality. In: Bunde, A., Havlin, S. (eds.) Fractals in Science. Springer, Berlin (1995)
7. Perelomov, A.: Generalized Coherent States and Their Applications. Springer,Berlin (1986)
8. Klauder, J.R., Skagerstam, B.: Coherent States. World Scientific, Singapore (1985)
9. Celeghini, E., De Martino, S., De Siena, S., Rasetti, M., Vitiello, G.: Quantum groups, coherent states, squeezing and lattice quantum mechanics. Annals of Physics 241, 50 (1995);Celeghini, E., Rasetti, M., Tarlini, M., Vitiello, G.: SU(1,1) Squeezed States as Damped Oscillators. Mod. Phys. Lett. B3, 1213 (1989); Celeghini, E., Rasetti, M., Vitiello, G.: On squeezing and quantum groups. Phys. Rev.Lett. 66, 2056 (1991)
10. Yuen, H.P.: Two-photon coherent states of the radiation field. Phys. Rev. 13, 2226 (1976)
11. Umezawa, H.: Advanced Field Theory: Micro, Macro and Thermal Physics. American Institute of Physics (1993)
12. Vitiello, G.: Defect Formation Through Boson Condensation in Quantum Field Theory. In: Bunkov, Y.M., Godfrin, H. (eds.) Topological Defects and the Non- Equilibrium Dynamics of Symmetry Breaking Phase Transitions. Kluwer Academic Press, Dordrecht (2000)
13. Iorio, A., Vitiello, G.: Quantum dissipation and quantum groups. Annals of Physics 241, 496 (1995)
14. Iorio, A., Vitiello, G.: Quantum groups and von Neumann theorem. Mod. Phys.Lett. B8, 269 (1995)
15. Freeman, W.J., Vitiello, G.: Brain dynamics, dissipation and spontaneous breakdown of symmetry. J. Phys. A: Math. Theor. 41, 304042 (2008),http://Select. iop.org.q-bio.NC/0701053v1
16. Freeman, W.J.: Origin, structure, and role of background EEG activity. Part 1.Analytic amplitude. Clin. Neurophysiol. 115, 2077 (2004)
17. Freeman, W.J.: Origin, structure, and role of background EEG activity. Part 2. Analytic phase. Clin. Neurophysiol. 115, 2089 (2004)
18. Braitenberg, V., Schuz, A.: Anatomy of the Cortex: Statistics and Geometry. Springer, Berlin (1991)
19. Linkenkaer-Hansen, K., Nikouline, V.M., Palva, J.M., Iimoniemi, R.J.: Long-range temporal correlations and scaling behavior in human brain oscillations. J. Neu-rosci. 15, 1370 (2001)
20. Hwa, R.C., Ferree, T.: Scaling properties of fluctuations in the human electroencephalogram. Phys. Rev. E 66, 021901 (2002)
21. Wang, X.F., Chen, G.R.: Complex networks: small-world, scale-free and beyond. IEEE Circuits Syst. 31, 6 (2003)
22. Freeman, W.J.: A field-theoretic approach to understanding scale-free neocortical dynamics. Biol. Cybern. 92(6), 350 (2005)
23. Franken, P., Malafosse, A., Tafti, M.: Genetic variation in EEG activity during sleep in inbred mice. Am. J. Physiol. 275, R1127 (1998)
24. Lyamin, O.I., Mukhametov, I.M., Siegel, J.M., Nazarenko, E.A., Polyakova, I.G., Shpak, O.V.: Unihemispheric slow wave sleep and the state of the eyes in a white whale. Behav. Brain Res. 129, 125 (2002)
25. Freeman, W.J., Vitiello, G.: Nonlinear brain dynamics as macroscopic manifestation of underlying many-body dynamics. Phys. of Life Reviews 3, 93 (2006)
26. Vitiello, G.: Dissipation and memory capacity in the quantum brain model. Int. J.Mod. Phys. B9, 973 (1995)