Self-Organization and Emergence

Heinz von Foerster 100

Organizing Institutions:

Heinz von Foerster Gesellschaft / Wien

ASC – American Society for Cybernetics

WISDOM – Wiener Institut für

sozialwissenschaftliche Dokumentation und Methodik

Institut für Zeitgeschichte | Universität Wien

AINS – Austrian Institute for Nonlinear Studies

Heinz von Foerster Gesellschaft / Wien

ASC – American Society for Cybernetics

WISDOM – Wiener Institut für

sozialwissenschaftliche Dokumentation und Methodik

Institut für Zeitgeschichte | Universität Wien

AINS – Austrian Institute for Nonlinear Studies

M. Sakellariadou*, A. Stabile° and G. Vitiello°^

Connes’ noncommutative spectral geometry and the seeds of quantization

*Department of Physics, King's College, University of London, Strand WC2R 2LS, London, U.K.

° Facoltà di Scienze and Gruppo Collegato I.N.F.N., Università di Salerno, I-84100 Salerno, Italy

A physical interpretation of the two-sheeted space, the most fundamental ingredient of the noncommutative spectral action, proposed by Connes as an approach to unification, is presented. It is shown that the doubling of the algebra is strictly related to dissipation. As a consequence, the doubling of the algebra is intimately related to the gauge structure of the theory. In a regime of completely deterministic dynamics, dissipation seems also to play a key role in the quantization of the theory, following 't Hooft's conjecture. It is thus argued that Connes' classical construction carries implicit in its feature of the doubling of the algebra the seeds of quantization [1].

[1] Phys. Rev. D 84, 045026 (2011) - arXiv:1106.4164

^ Presented by G. Vitiello

e-mail:

mairi.sakellariadou@kcl.ac.uk

anstabile@gmail.com

vitiello@sa.infn.it

GIUSEPPE VITIELLO

Facolta' di Scienze, Universita' di Salerno - 84084 Fisciano (Salerno), Italy

e-mail: vitiello@sa.infn.it

Full Professor (Professore Ordinario) of Theoretical Physics, University of Salerno

Ph.D. in Physics, University of Wisconsin, Milwaukee, USA, 1974 (Supervisor Prof. Hiroomi Umezawa)

Laurea in Fisica, Universita' di Napoli, Italy, 1970 (Supervisor Prof. Francesco Guerra)

Associate researcher INFN (Istituto Nazionale di Fisica Nucleare)

Research activity in: Quantum field theory, gauge theories, non-linear dynamical systems, biological systems and brain physics.

Author of about 140 papers in international journals, of 20 chapters in monographic volumes, of 60 reports in Conference Proceedings.

Serving as referee for several Journals (Physical Review Letters, Physical Review, Physics Letters A and B, Europhysics Letters, Annals of Physics, J.Phys. A:Math.Gen., Physica Scripta, etc.).

Member of several Scientific Advisory Boards and Organizing Committee of International Conferences and Workshops.

A list of publications can be found at: http://www.sa.infn.it/giuseppe.vitiello

BOOKS

. Hiroomi Umezawa and Giuseppe Vitiello, "Quantum Mechanics", Bibliopolis, Napoli 1986.

Translated in Japanese by K.Yasue and M.Jibu, Nippon Hyoron Sha. Co.Ltd., Tokyo, Japan 2005.

. G.Globus, K.H.Pribram, G.Vitiello (Editors) “Brain and Being. At the boundary between science,

philosophy, language and arts” John Benjamins Publ. Co., Amsterdam 2004.

. Giuseppe Vitiello, "My Double Unveiled - The dissipative quantum model of brain", John Benjamins Publ.

Co., Amsterdam 2001.

. Massimo Blasone, Petr Jizba and Giuseppe Vitiello, "Quantum Field Theory and its macroscopic

manifestations", Imperial College Press, London 2011.