Symmetries, variational principles, and quantum dynamics
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'...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/S1026022604310022 |
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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |