An Introduction to κ-Deformed Symmetries, Phase Spaces and Field Theory

In this review, we give a basic introduction to the κ-deformed relativistic phase space and free quantum fields. After a review of the κ-Poincaré algebra, we illustrate the construction of the κ-deformed phase space of a classical relativistic particle using the tools of Lie bi-algebras and Poisson–Lie groups. We then discuss how to construct a free scalar field theory on the non-commutative κ-Minkowski space associated to the κ-Poincaré and illustrate how the group valued nature of momenta affects the field propagation.