SPONTANEOUS BREAKING OF LORENTZ SYMMETRY AND VERTEX OPERATORS FOR VORTICES.

We first review the spontaneous Lorentz symmetry breaking in the presence of mass-less gauge fields and infraparticles. This result was obtained long time ago in the context of rigorous quantum field theory (QFT) by Frohlich, Morchio and Strocchi [Ann. Phys. 119, 241 (1979); Phys. Lett. B 89, 61 (1979)] and reformulated by Balachandran and Vaidya (arXiv:1302.3406) using the notion of superselection sectors and direction-dependent test functions at spatial infinity for gauge transformations. Inspired by these developments and under the assumption that the spectrum of the electric charge is quantized (in units of a fundamental charge e). we construct a family of vertex operators which create winding number A;, electrically charged Abelian vortices from the vacuum (zero winding number sector) and/or shift the winding number by k units. Vortices created by this vertex operator may be viewed both as a source and as a probe for inducing and detecting the breaking of spontaneous Lorentz symmetry. We find that for rotating vortices, the vertex operator at level k shifts the angular momentum of the vortex by kq/q, where q is the electric charge of the quantum state of the vortex and q is the charge of the vortex scalar field under the U(l) gauge field. We also show that, for charged-particle-vortex composites, angular momentum eigenvalues shift by kq/q being the electric charge of the charged-particle-vortex composite. This leads to the result that for q/q half-odd integral and for odd k, our vertex operators flip the statistics of charged-particle-vortex composites from bosons to ferrnions and vice versa. For fractional values of q/q, application of vertex operator on charged-particle-vortex composite leads in general to composites with anyonic statistics. [ABSTRACT FROM AUTHOR]