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Mathematics

Journal of Generalized Lie Theory and Applications

Author(s): Dimitri Gurevich, Pavel Saponov

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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.

This article was published in Institute for Problems of Information Transmission and referenced in Journal of Generalized Lie Theory and Applications

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