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Constraints and degrees of freedom in Lorentz-violating field theories

机译：违反洛伦兹领域理论的约束和自由度

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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. To obtain a tensor field with this behavior, one can posit a smooth potential for this field, in which case it would be expected to lie near the minimum of its potential. Alternately, one can enforce a nonzero tensor value via a Lagrange multiplier. The present work explores the relationship between these two types of theories in the case of vector models. In particular, the na?ve expectation that a Lagrange multiplier “kills off” 1?degree of freedom via its constraint does not necessarily hold for vector models that already contain primary constraints. It is shown that a Lagrange multiplier can only reduce the degrees of freedom of a model if the field-space function defining the vacuum manifold commutes with the primary constraints.
机译：当前许多“违反洛伦兹对称性”的模型都是通过采用真空期望值的矢量或张量场来做到这一点的，从而自发地破坏了拉格朗日的潜在洛伦兹对称性。为了获得具有这种行为的张量场，可以为该场设定一个平滑的电位，在这种情况下，可以预期它位于其电位的最小值附近。或者，可以通过拉格朗日乘数强制非零张量值。在矢量模型的情况下，本工作探讨了这两种类型的理论之间的关系。特别是，对拉格朗日乘数通过其约束“杀死” 1？自由度的幼稚期望不一定适用于已经包含主要约束的矢量模型。结果表明，如果定义真空歧管的场-空间函数与主要约束条件互换，则拉格朗日乘数只能降低模型的自由度。

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