On problems in quantum field theory of superluminal neutrino

One of the main assertions of special relativity theory which is a cornerstone of modern fundamental physics is the assertion that the maximal velocity of propagation of perturbations does not exceed the velocity of light in vacuum. Important contributions to the development of special and general relativity theories made not only physicists Einstein, Lorentz and others but also mathematicians Poincare, Minkowsky, Hilbert, E. Cartan, H. Weil and others.
On 23-rd October 2011 the collaboration OPERA announced the results of experiments according to which the velocity of propagation of neutrino exceeds the velocity of light in vacuum. Of cource this extraordinary claim requires careful scrutinize and performing of independent experiments; it is still possible that the claim will be disproved. However, if the superluminal neutrino do exist then it would require a serious modification of modern physical and mathematical models of spacetime and quantum field theory.
In the talk there will be discussed mathematical and physical problems which appear in quantum field theory if one admits the existence of superluminal signals and also some suggested solutions of these problems.
References to some recent works on this subject can be found in a note by the speakers arXiv: 1110.0456v1, where a possible solution of the problem of unstability of superluminal neutrinos posed by Cohen and Glashow is proposed.