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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| Format: | Article |
| Language: | English |
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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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| author | J. Manjavidze A. Sissakian |
| author_facet | J. Manjavidze A. Sissakian |
| author_sort | J. Manjavidze |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e22de861129f412981d8740926aa1e7a |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e22de861129f412981d8740926aa1e7a2025-02-03T00:59:35ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2004-01-012004120521210.1155/S1026022604310022Symmetries, variational principles, and quantum dynamicsJ. Manjavidze0A. Sissakian1Joint Institute for Nuclear Research (JINR), Moscow Region, Dubna 141980, RussiaJoint Institute for Nuclear Research (JINR), Moscow Region, Dubna 141980, RussiaWe 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.http://dx.doi.org/10.1155/S1026022604310022 |
| spellingShingle | J. Manjavidze A. Sissakian Symmetries, variational principles, and quantum dynamics Discrete Dynamics in Nature and Society |
| title | Symmetries, variational principles, and quantum dynamics |
| title_full | Symmetries, variational principles, and quantum dynamics |
| title_fullStr | Symmetries, variational principles, and quantum dynamics |
| title_full_unstemmed | Symmetries, variational principles, and quantum dynamics |
| title_short | Symmetries, variational principles, and quantum dynamics |
| title_sort | symmetries variational principles and quantum dynamics |
| url | http://dx.doi.org/10.1155/S1026022604310022 |
| work_keys_str_mv | AT jmanjavidze symmetriesvariationalprinciplesandquantumdynamics AT asissakian symmetriesvariationalprinciplesandquantumdynamics |