Complex scalar field in $κ$-Minkowski spacetime

Abstract: It is often expected that one cannot treat spacetime as a continuous manifold as the Planck scale is approached, because of to possible effects due to a quantum theory of gravity. There have been several proposals to model such a deviation from the classical behaviour, one of which is noncommutativity of spacetime coordinates. In this context, the non-commutativity scale is seen as an observer-independent length scale. Of course, such a scale impose a modification of ordinary relativistic symmetries, which now need to be deformed to accommodate this fundamental scale. The $\kappa$-Poincar\'e algebra is an example of this deformation. In what follows I will briefly describe a construction of a $\kappa$-deformed complex scalar field theory, while at the same time shedding light on the behaviour of discrete and continuous symmetries in this formalism. This in turn will open the way to the study of the application of this formalism to actual physical processes. I will then conclude with some comments and prospects for the future.