QUANTUM MECHANICS ON THE CIRCLE THROUGH HOPF Q-DEFORMATIONS OF THE KINEMATICAL ALGEBRA WITH POSSIBLE APPLICATIONS TO LÉVY PROCESSES
作者： V.K. DOBREV , H.-D. DOEBNER , R. TWAROCK
DOI: 10.1142/9789812702104_0011
关键词:
摘要: A formulation of quantum mechanics on S' or its N-point discretisation Sh based different types q-deformations subalgebras the kinematical algebra system was discussed ( [l]) in framework Bore1 quantisation. We review this method and introduce new Hopf full algebra, i.e. both position momentum observable. The implications deformed approach to dynamics resulting evolution equations is assessed compared with previous results including non-deformed case. presented algebraic for can be translated LBvy processes structures related evolutions; possible applications are outlined.
sci-hub.se 参考文章(15)
B. Angermann, H. D. Doebner, J. Tolar, Quantum kinematics on smooth manifolds Non-linear Partial Differential Operators and Quantization Procedures. pp. 171- 208 ,(1983) , 10.1007/BFB0073173
Michael Schürmann, White Noise on Bialgebras ,(1993)
H.-D. Doebner, J. D. Hennig, A Quantum Mechanical Evolution Equation for Mixed States from Symmetry and Kinematics Symmetries in Science VIII. pp. 85- 90 ,(1995) , 10.1007/978-1-4615-1915-7_8
Uwe Franz, René Schott, Stochastic Processes and Operator Calculus on Quantum Groups Springer Netherlands. ,(1999) , 10.1007/978-94-015-9277-2
P. Nattermann, W. Scherer, A.G. Ushveridze, Exact solutions of the general Doebner-Goldin equation Physics Letters A. ,vol. 184, pp. 234- 240 ,(1994) , 10.1016/0375-9601(94)90381-6
H D Doebner, G A Goldin, Properties of nonlinear Schrodinger equations associated with diffeomorphism group representations Journal of Physics A. ,vol. 27, pp. 1771- 1780 ,(1994) , 10.1088/0305-4470/27/5/036
Luigi Accardi, Michael Schürmann, Wilhelm von Waldenfels, Quantum independent increment processes on superalgebras Mathematische Zeitschrift. ,vol. 198, pp. 451- 477 ,(1988) , 10.1007/BF01162868
R Twarock, V.K Dobrev, H.-D Doebner, Quantum mechanics with difference operators Reports on Mathematical Physics. ,vol. 50, pp. 409- 431 ,(2002) , 10.1016/S0034-4877(02)80069-6
Michael Schürmann, A class of representations of involutive bialgebras Mathematical Proceedings of the Cambridge Philosophical Society. ,vol. 107, pp. 149- 175 ,(1990) , 10.1017/S0305004100068432
R Twarock, A q-Schrödinger equation based on a Hopf q-deformation of the Witt algebra Journal of Physics A. ,vol. 32, pp. 4971- 4981 ,(1999) , 10.1088/0305-4470/32/26/315