Wave Operators on Quantum Algebras via Noncanonical Quantization |
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Authors: | Dimitri Gurevich Pavel Saponov |
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Institution: | 1.LAMAV,Université de Valenciennes,Valenciennes,France;2.Division of Theoretical Physics,IHEP,Protvino,Russia |
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Abstract: | We suggest a method to quantize basic wave operators of Relativistic Quantum Mechanics (Laplace, Maxwell, Dirac ones) without
using canonical coordinates. We define two-parameter deformations of the Minkowski space algebra and its 3-dimensional reduction
via the so-called Reflection Equation Algebra and its modified version. Wave operators on these algebras are introduced by
means of quantized partial derivatives described in two ways. In particular, they are given in so-called pseudospherical form
which makes use of a q-deformation of the Lie algebra sl(2) and quantum versions of the Cayley-Hamilton identity. |
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Keywords: | |
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