In this thesis I study various aspects of theories in the two most studied examples of noncommutative spacetimes: canonical spacetime ($[x_{ \mu},x_{ \nu}]=\theta_{ \mu\nu}$) and $\kappa$-Minkowski spacetime ($[x_{ i},t]=\kappa^{ -1} x_{ i}$). In the first part of the thesis I consider the description of the propagation of "classical" waves in these spacetimes. In the case of $\kappa$-Minkowski this description is rather nontrivial, and its phenomenological implications are rather striking. In the second part of the thesis I examine the structure of quantum field theory in noncommutative spacetime, with emphasis on the simple case of the canonical spacetime. I find that the so-called IR/UV mixing can affect significantly the phase structure of a quantum field theory and also forces us upon a certain revision of the strategies used in particle-physics phenomenology to constrain the parameters of a model.
Categories: hep-th