Singular Hamiltonians in models with spontaneous Lorentz symmetry breaking

摘要

Many current models which “violate Lorentz symmetry” do so via a vector or tensor field which takes on a vacuum expectation value, thereby spontaneously breaking the underlying Lorentz symmetry of the Lagrangian. One common way to construct such a model is to posit a smooth potential for this field; the natural low-energy solution of such a model would then be excepted to have the tensor field near the minimum of its potential. It is shown in this work that some such models, while appearing well posed at the level of the Lagrangian, have a Hamiltonian which is singular on the vacuum manifold and are therefore ill posed. I illustrate this pathology for an antisymmetric rank-2 tensor field and find sufficient conditions under which this pathology occurs for more general field theories.