Towards an interpretation of spontaneous Lorentz symmetry breaking in modified BF theories

Abstract

In (1+1) dimensions we consider a BF model defined by B = Φμdxμ and F = d∧X, further extended by a potential V(Φ2) designed to trigger spontaneous Lorentz symmetry breaking in the system. We review the general derivation of the Goldstone theorem and we study the propagation of the corresponding Goldstone modes starting from the linearized version of the model. We use two different approaches to discuss the symmetry breaking: (1) in the first case we start from an arbitrary potential having a minimum at Φμ = Cμ and we study the excitations φμ around the minimum which contain the resulting Goldstone modes. (2) in the second approach we freeze the non Goldstone modes by restricting the field Φμ to the orbit of the vacuum via a Lagrange multiplier. The case of a bumblebee model in (1+1) dimensions is reviewed for comparison purposes.