Origin of spontaneous violation of the Lorentz symmetry: Vortices in the cosmos

Abstract

By carefully studying the (1,0)+(0,1) representation space for massive particles we point to the existence of certain inherent tachyonic dispersion relations: E^2= p^2-m^2. We put forward an interpretation that exploits these ``negative mass squared'' solutions; rotational invariance is spontaneously broken. Relevance of these results to the vortices in the cosmos is pointed out. NOTE: Just as "negative energy solutions'' of Dirac equation are re-interpreted as antiparticles, similarly the possibility exists for re-interpreting the tachyonic dispersion relations of all (j,0)+(0,j) representation spaces via spontaneous Lorentz symmetry breaking. In Mod. Phys. Lett. A8:2623-2630,1993 we exhibited this explicitly for the j=1 representation space. The interest in this old subject has grown markedly in recent years as is evident from numerous theoretical and phenomenological works on the subject. With this observation, we make this replacement of our paper fourteen years after its initial publication. The Abstract and main text remain unaltered. The title is changed to reflect the underlying physics more closely.