Singular Hamiltonians in models with spontaneous Lorentz symmetry breaking

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.

11 pages

References in corpus (8)

• Signals for Lorentz Violation in Post-Newtonian Gravity
• Stability of spherically symmetric solutions in modified theories of gravity
• Vector models of gravitational Lorentz symmetry breaking
• Dynamical Lorentz symmetry breaking in a tensor bumblebee model
• A monopole solution in a Lorentz-violating field theory
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Cited by in corpus (5)

• 3+1 Formulation of the Standard-Model Extension Gravity Sector
• Modified-gravity theories with nondynamical background fields
• Spontaneous symmetry breaking in models with second-class constraints
• Bumblebee gravity: spherically-symmetric solutions away from the potential minimum
• Covariant Quantum Gravitational Corrections to Scalar and Tensor Field Models