Abstract
The mechanism of the dynamical rearrangement of symmetry in quantum field theory underlies the phenomenon of coherent boson condensation in the vacuum state. Coherent states appear to be related to fractal self-similarity. The dynamical paradigm of coherence opens the way to an integrated vision of natural phenomena and it may possibly rule morphogenetic processes. Robustness properties of physical systems, such as dynamical and functional robustness, topological robustness, multilevel and semantic robustness may find their root in coherence. Possible extension to biology and neuroscience is discussed.
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Notes
- 1.
The word morphogenesis is thus defined by specific mathematical QFT quantities. Its relation with other definitions or uses, in a qualitative or quantitative way, in other disciplines is not object of discussion here. The comparison among different definitions in different context does not belong to the task of this paper and therefore I will not discuss it.
- 2.
These conclusions hold also when a gauge field (e.g. in electrodynamics, in the electro-weak interaction of the standard model and in the quantum chromodynamics) is present. In such a case the condensation of NG bosons still characterizes the ground state and its robustness properties. The NG bosons do not belong to the spectrum of observable particles and the gauge field, which acquires a non-vanishing mass , is confined to self-focusing channels (the so called Anderson-Higgs-Kibble mechanism) (Itzykson and Zuber 1980; Umezawa 1993; Blasone et al. 2011). Such a self-focusing of the gauge field propagation is another manifestation of the robustness of the system in recovering the original dynamical invariance.
- 3.
Such an observation has led to a possible mathematical formulation, within the Chomsky Generative Grammar approach, of the formation of concepts out of syntactic elements in linguistics (Piattelli-Palmarini and Vitiello 2015).
- 4.
An illustrative example of topological charge is the one of the kink solution in one-dimensional nonlinear dynamics. The kink is characterized by the hyperbolic tangent tgh x, whose limits at x → ±∞ are ±1, respectively, so that the topological charge Q is in this case defined by Q = ½(tgh x |+∞ – tgh x|-∞) = 1. In the case of a vortex solution the topological charge is given by the number of “turns” around the vortex core and is called the winding number.
- 5.
Quotation marks in the original text.
- 6.
Quotation marks in the original text.
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Acknowledgments
I thank the anonymous referee and the Editors of this volume for their suggestions and help. Of course, the responsibility of statements and positions presented in this paper is only mine. I am glad to dedicate this work to the memory of Walter J. Freeman in the occasion of one year since his departure and to celebrate the wisdom of Antonio Gramsci on the 80th year since his tragic death.
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Vitiello, G. (2018). Dynamical Rearrangement of Symmetry and Robustness in Physics and Biology. In: Bertolaso, M., Caianiello, S., Serrelli, E. (eds) Biological Robustness. History, Philosophy and Theory of the Life Sciences, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-030-01198-7_12
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