Abstract
Symmetries play a major theoretical role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century.
We first present a few examples of how symmetries allow to objectivize physical phenomena and then a short survey of conceptual and technical aspects of symmetries and symmetry breakings, beginning by the role played by Galileo’s group in the construction of space in modern physics. Then, we provide an account of Noether’s theorem, which relates invariant quantities and symmetries. A short, but general classification of symmetry breaking in physics follows. Our purpose is to describe some aspects of spontaneous symmetry breakings, in order to introduce critical transitions in the next chapter, where these breakings apply. Last, we will propose a link between randomness and symmetry breaking.
This brief overview will allow us to draw some preliminary conclusions as well as hints towards our project, in particular concerning the distinctive consequences associated to continuous and discrete symmetries and their breakings. We will also understand, at least partially, why symmetry breaking is associated to specific features, such as singularities, and the loss of “standard” behavior in classical physical dynamics. This will help us to open towards our analysis of the critical singularity of life.
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© 2014 Springer-Verlag Berlin Heidelberg
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Longo, G., Montévil, M. (2014). Symmetry and Symmetry Breakings in Physics. In: Perspectives on Organisms. Lecture Notes in Morphogenesis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35938-5_5
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DOI: https://doi.org/10.1007/978-3-642-35938-5_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35937-8
Online ISBN: 978-3-642-35938-5
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