Acta Applicandae Mathematicae

, Volume 109, Issue 1, pp 19–38 | Cite as

Wave Operators on Quantum Algebras via Noncanonical Quantization

  • Dimitri GurevichEmail author
  • Pavel Saponov


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.


Wave operators Laplace operator Maxwell operator Dirac operator Noncanonical quantization Braiding Hecke symmetry (Truncated) q-Minkowski space q-derivatives Braided vector fields 

Mathematics Subject Classification (2000)

17B37 81R50 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.LAMAVUniversité de ValenciennesValenciennesFrance
  2. 2.Division of Theoretical PhysicsIHEPProtvinoRussia

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