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.
Highlights
The prospect of finding new physics via Lorentz symmetry violation has been of significant interest over the past couple of decades
Lorentz symmetry is broken spontaneously; one postulates the existence of a new fundamental field that is not a Lorentz scalar and assigns dynamics to this field that obey Lorentz symmetry but lead it to take on a nonzero “vacuum expectation value.”
In the presence of a Yukawa-like couplings between this new field and conventional matter fields, the results of experiments would depend on the relative orientation in spacetime of the observer’s 4-velocity and the new field, leading to framedependent effects
Summary
The prospect of finding new physics via Lorentz symmetry violation has been of significant interest over the past couple of decades In many such models, Lorentz symmetry is broken spontaneously; one postulates the existence of a new fundamental field that is not a Lorentz scalar and assigns dynamics to this field that obey Lorentz symmetry but lead it to take on a nonzero “vacuum expectation value.”. Many (though not all) of the above-cited models share two features They accomplish the spontaneous breaking of Lorentz symmetry by assigning a potential energy VðΨÁÁÁÞ to some Lorentz tensor ΨÁÁÁ. The symbol δ will generally denote either variations of functionals or functional derivatives
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