Tomasz Trześniewski
On the E ffective Dimension of Spacetime
In the recent decades the theoretical physics gave rise to many ideas which are challenging the long-standing concepts. Such propositions are especially numerous in the regime of the hypothetical quantum gravity. One example is the prediction that in the very small scales, presumably close to the Planck length/time, the eff ective dimension of spacetime can be di fferent than 4. I will begin with the de finitions of the Hausdor ff and spectral dimension and then present the spectrum of results obtained in a variety of approaches to the quantum gravity. I will particularly concentrate on the models with the deformed relativistic symmetries and the associated curved momentum space.