Discrete Dynamics in Nature and Society

Discrete Dynamics in Nature and Society / 2004 / Article
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In memory of Ilya Prigogine

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Volume 2004 |Article ID 949021 | https://doi.org/10.1155/S1026022604310022

J. Manjavidze, A. Sissakian, "Symmetries, variational principles, and quantum dynamics", Discrete Dynamics in Nature and Society, vol. 2004, Article ID 949021, 8 pages, 2004. https://doi.org/10.1155/S1026022604310022

Symmetries, variational principles, and quantum dynamics

Received15 Oct 2003


We describe the role of symmetries in formation of quantum dynamics. A quantum version of d'Alembert's principle is proposed to take into account the symmetry constrains more exact. It is argued that the time reversibility of quantum process, as the quantum analogy of d'Alembert's principle, makes the measure of the corresponding path integral δ-like. The argument of this δ-function is the sum of all classical forces of the problem under consideration plus the random force of quantum excitations. Such measure establishes the one-to-one correspondence with classical mechanics and, for this reason, allows a free choice of the useful dynamical variables. The analysis shows that choosing the action-angle variables, one may get to the free-from-divergences quantum field theory. Moreover, one can try to get an independence from necessity to extract the degrees of freedom constrained by the symmetry. These properties of new quantization scheme are vitally essential for such theories as the non-Abelian Yang-Mills gauge theory and quantum gravity.

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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