Spontaneous Lorentz symmetry breaking
Lorentz symmetry is one of the cornerstones of our current knowledge of the elementary interactions. However, the quantum gravity problem suggests that the structure of space-time might be fundamentally different from what we know at the Planck scale: this might even imply in small modifications/violations of the Lorentz symmetry. These Lorentz violations might have effects even in low energy physics (compared with the Planck energy), and are described by an effective field theory known as the Standard Model Extension (SME). In this formalism, it is natural to assume that the Lorentz symmetry breaking is spontaneous: actually, the gravitational sector of the SME currently can only be consistently formulated in this case. The mechanism of spontaneous breaking of global and local symmetries is already well known, being one of the fundamental ingredients of the Standard Model of elementary particles, for example. Our objective is to study in more detail the application of this mechanism to induce the Lorentz symmetry breaking in low energy physics.