Abstract
We show that effects of retardation in processes of quasiparticle generation and destruction can be reduced to a deformation of the communication relations for the quasiparticle creation (annihilation) operators. In such an approach the deformation parameter is determined by a retardation time. Similar deformed commutation relations were proposed by Borisov, Ilinski and Uzdin [Phys. Lett. A 169 (1992) 427] when studying the classical and quantum dynamics for the particles in the quantum group representation space. Some generalizations of the deformed commutation relations are given and their physical sense is discussed. Physical problems related to such objects are described.
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