This monograph provides an introduction to deformations of Poincaré symmetries focusing on models with a Lie group momentum space and associated non-commutative space-times. The emphasis is put on the emergence of such structures from quantum gravity, their mathematical features described in terms of Hopf algebras and applications to particle kinematics and field theory.Part I of this work focuses on the link between gravity and deformed symmetries in the case of 2+1 and 3+1 space-time dimensions. Part II is devoted to the description of classical particles with group valued momenta, their phase spaces and kinematics. The last part of these notes provides an introduction to the basic features of classical and quantum field theory on -Minkowski space-time, the prototypical example of non-commutative space-time exhibiting deformed Poincaré symmetry.

The text, being the first providing a detailed overview of these topics, is primarily intended for researchers and graduatestudents interested in non-commutative field theories and quantum gravity phenomenology.

Autorentext

Michele Arzano is a researcher in theoretical physics at the University of Naples "Federico II". He obtained his PhD from the University of North Carolina at Chapel Hill and has held positions at the Perimeter Institute for Theoretical Physics in Canada, at the Institute for Theoretical Physics at Utrecht University in the Netherlands and at "Sapienza" University of Rome in Italy. His research interests over the years have ranged from non-commutative field theory and deformed symmetries to quantum effects in curved spacetimes and black hole thermodynamics. More recently he has contributed to research on asymptotic symmetries in general relativity and conformal quantum mechanics.

Jerzy Kowalski-Glikman is a professor at the Institute of Theoretical Physics of the University of Wroclaw and at National Centre for Nuclear Research in Warsaw. He got his PhD in 1985 from the University of Warsaw and habilitation in 1994 from the University of Wroclaw and full professorship in 2002. His research interests include quantum gravity and quantum gravity phenomenology, non-commutative field theories, cosmology, and string theory. He is author of more than hundred research papers published on international peer reviewed journals.