The Centrally Extended Heisenberg Algebra and Its Connection with the Schroedinger, Galilei and Renormalized Higher Powers of Quantum White Noise Lie Algebras
In previous papers we have shown that the one mode Heisenberg algebra Heis(1) admits a unique non-trivial central extensions CeHeis(1) which can be realized as a sub-Lie-algebra of the Schroedinger algebra, in fact the Galilei Lie algebra. This gives a natural family of unitary representations of Ce...
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| Veröffentlicht in: | AIP conference proceedings 2010-06, Vol.1243 (1) |
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| creator | Accardi, Luigi Boukas, Andreas |
| description | In previous papers we have shown that the one mode Heisenberg algebra Heis(1) admits a unique non-trivial central extensions CeHeis(1) which can be realized as a sub-Lie-algebra of the Schroedinger algebra, in fact the Galilei Lie algebra. This gives a natural family of unitary representations of CeHeis(1) and allows an explicit determination of the associated group by exponentiation. In contrast with Heis(1), the group law for CeHeis(1) is given by nonlinear (quadratic) functions of the coordinates. The vacuum characteristic and moment generating functions of the classical random variables canonically associated to CeHeis(1) are computed. The second quantization of CeHeis(1) is also considered. |
| doi_str_mv | 10.1063/1.3460157 |
| format | Article |
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This gives a natural family of unitary representations of CeHeis(1) and allows an explicit determination of the associated group by exponentiation. In contrast with Heis(1), the group law for CeHeis(1) is given by nonlinear (quadratic) functions of the coordinates. The vacuum characteristic and moment generating functions of the classical random variables canonically associated to CeHeis(1) are computed. 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This gives a natural family of unitary representations of CeHeis(1) and allows an explicit determination of the associated group by exponentiation. In contrast with Heis(1), the group law for CeHeis(1) is given by nonlinear (quadratic) functions of the coordinates. The vacuum characteristic and moment generating functions of the classical random variables canonically associated to CeHeis(1) are computed. 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| source | AIP Journals |
| subjects | ALGEBRA CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS DIFFERENTIAL EQUATIONS EQUATIONS FUNCTIONAL ANALYSIS HEISENBERG PICTURE LIE GROUPS MATHEMATICS MECHANICS NONLINEAR PROBLEMS PARTIAL DIFFERENTIAL EQUATIONS PHYSICS OF ELEMENTARY PARTICLES AND FIELDS QUANTIZATION QUANTUM MECHANICS RANDOMNESS RENORMALIZATION SCHROEDINGER EQUATION SECOND QUANTIZATION SYMMETRY GROUPS WAVE EQUATIONS |
| title | The Centrally Extended Heisenberg Algebra and Its Connection with the Schroedinger, Galilei and Renormalized Higher Powers of Quantum White Noise Lie Algebras |
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