Broken Lorentz invariance and metric description of interactions in a deformed Minkowski space

We discuss the possible breakdown of Lorentz invariance-at distances greate r than the planck length-from both the theoretical and the phenomenological point of view. The theoretical tool to deal with such a problem is provide d by a "deformation" of the Minkowski metric, with parameters dependent on the energy of the physical system considered. Such a deformed metric realiz es, for any interaction, the "solidarity principle" between interactions an d spacetime geometry (usually assumed for gravitation), according to which the peculiar features of every interaction determine locally-its own spacet ime structure. The generalized theory of relativity, based on the locally d eformed Minkowski spacetime, is called "deformed special relativity" (DSR). In the first part of the paper, we give the foundations and the basic laws of DSR. In the second part, we analyse some experimental data, which admit an interpretation in terms of the DSR formalism and are, therefore, candid ates for displaying a breakdown of the Lorentz symmetry. They are (i) the s uperluminal propagation of evanescent electromagnetic waves in waveguides, (ii) the meanlife of the K-S(n). (iii) the Bose-Einstein correlation in pio n production and (iv) the comparison of clock rates in the gravitational fi eld of Earth. Such analysis provides us with the explicit forms of the rela ted deformed metrics as functions of the energy, thus putting in evidence, in all four cases (and therefore for all four fundamental interactions), de partures from the usual Minkowski metric. This preliminary evidence for a b roken Lorentz invariance may be regarded as the signature of possible nonlo cal effects involved in the processes examined. Moreover the corresponding deformed metrics obtained by our analysis provide as effective dynamical de scription of the interactions (at least in the energy range considered).