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The Mathematical Description of a Generic Physical System

Zalamea, Federico (2015) The Mathematical Description of a Generic Physical System. Topoi. pp. 1-10. ISSN 1572-8749

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Abstract

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 struc- tures’’. If one imposes the condition that these mathemat- ical 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 physi- cist’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 pro- vides tools to overcome this tension and to define physical properties.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Zalamea, Federicofedericozalamea@gmail.com
Keywords: Quantum Mechanics; Structuralism; Group Theory; Individuation
Subjects: Specific Sciences > Physics
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Mr Federico Zalamea
Date Deposited: 04 Jul 2015 14:06
Last Modified: 04 Jul 2015 14:06
Item ID: 11533
Journal or Publication Title: Topoi
Publisher: Spirnger
Official URL: http://link.springer.com/article/10.1007%2Fs11245-...
DOI or Unique Handle: 10.1007/s11245-015-9322-7
Subjects: Specific Sciences > Physics
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Symmetries/Invariances
Date: 2015
Page Range: pp. 1-10
ISSN: 1572-8749
URI: http://philsci-archive.pitt.edu/id/eprint/11533

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