, Volume 34, Issue 2, pp 339–348 | Cite as

The Mathematical Description of a Generic Physical System

  • Federico Zalamea


When dealing with a certain class of physical systems, the mathematical characterization of a generic system aims to describe the phase portrait of all its possible states. Because they are defined only up to isomorphism, the mathematical objects involved are “schematic structures”. If one imposes the condition that these mathematical definitions completely capture the physical information of a given system, one is led to a strong requirement of individuation for physical states. However, we show there are not enough qualitatively distinct properties in an abstract Hilbert space to fulfill such a requirement. It thus appears there is a fundamental tension between the physicist’s purpose in providing a mathematical definition of a mechanical system and a feature of the basic formalism used in the theory. We will show how group theory provides tools to overcome this tension and to define physical properties.


Group theory Individuation Quantum mechanics Structuralism 



This work has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013 Grant Agreement No 263523). I also want to thank Gabriel Catren, Julien Page, Christine Cachot, Michael Wright and Fernando Zalamea for helpful discussions and comments on earlier drafts of this paper.


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Laboratoire SPHERE, UMR 7219CNRS—Université Paris DiderotParis Cedex 13France

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