q-Deformation of algebraic structures of quantum and classical mechanics |
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Authors: | Debendranath Sahoo M C Valsakumar |
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Institution: | (1) Theoretical Studies Section, Materials Science Division, Indira Gandhi Centre for Atomic Research, 603 102 Kalpakkam, India |
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Abstract: | There exists a coassociative and cocommutative coproduct in the linear space spanned by the two algebraic products of a classical
Hamilton algebra (the algebraic structure underlying classical mechanics 1]). The transition from classical to quantum Hamilton
algebra (the algebraic structure underlying quantum mechanics) is anħ-deformation which preserves not only the Lie property of the classical Hamilton algebra but also the coassociativity and
cocommutativity of the above coproduct. By explicit construction we obtain the algebraic structures of theq-deformed Hamilton algebras which preserve the said properties of the coproduct. Some algorithms of these structures are obtained
and their implications discussed. The problem of consistency of time evolution with theq-deformed kinematical structure is discussed. A characteristic distinction between the parametersħ andq is brought out to stress the fact thatq cannot be regarded as a fundamental constant. |
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Keywords: | Classical Hamiltonian algebra quantum Hamiltonian algebra quantum mechanics classical mechanics |
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