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arXiv · 1903.06140

Singular Hamiltonians in models with spontaneous Lorentz symmetry breaking

Michael D. Seifert
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Abstract

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.

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Michael D. Seifert. 2019-03-14. Singular Hamiltonians in models with spontaneous Lorentz symmetry breaking. https://doi.org/10.1103/physrevd.100.065017

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