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Issue 42, 2009
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Generalization of the continuous symmetry measure: the symmetry of vectors, matrices, operators and functions

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Abstract

In this paper we generalize a method for evaluating the continuous symmetry measure, which is a quantitative estimate of the degree of symmetry of a given object. The generalization makes it possible to calculate the degree of symmetry content for any mathematical entity that is part of metric spaces such as vectors, matrices, operators and functions. Furthermore, by this new approach one can calculate the symmetry-content values for any compact symmetry groups either finite or infinite. An advantage of the new methodology is the ability to investigate analytically problems of symmetry changes. Examples of symmetry evaluation calculations are provided, including mixing of ideal gases, evaluation of the symmetry content of a Hamiltonian operator, the 2pz orbital of the hydrogen atom, and more.

Graphical abstract: Generalization of the continuous symmetry measure: the symmetry of vectors, matrices, operators and functions

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Publication details

The article was received on 08 Jun 2009, accepted on 23 Jul 2009 and first published on 19 Aug 2009


Article type: Paper
DOI: 10.1039/B911179D
Citation: Phys. Chem. Chem. Phys., 2009,11, 9653-9666
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    Generalization of the continuous symmetry measure: the symmetry of vectors, matrices, operators and functions

    C. Dryzun and D. Avnir, Phys. Chem. Chem. Phys., 2009, 11, 9653
    DOI: 10.1039/B911179D

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