prof. dr hab. Jerzy Lukierski

Quantum Deformations of Space-Time and Deformations of String Backgrounds

The aim of my talk is threefold: 1) To recall the appearance of noncommutative space-time ("quantum space-time") in context of quantization of gravity. 2) To show the use of classical r-matrices defined for space-time symmetry algebras for the classification of possible quantum space-times. 3) To employ the classical r-matrices to the description of deformations of dynamical models, in particular: -- a) in field theory - to the introduction of star-product multiplication of deformed fields, -- b) in string theory - to the deformation of string actions represented as two-dimensional sigma models (deformed string actions <- -> Yang-Baxter sigma models). The aims 2) and 3) were investigated in three publications which appeared in October and November 2015 (arXiv:1510.09125, arXiv:1510.03083, arXiv:1511.03653).