Constraints and degrees of freedom in Lorentz-violating field theories

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. 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 non-zero 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 naïve expectation that a Lagrange multiplier "kills off" one 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.

11 pages. v2: added discussion of previous work in Ref. [19]

References in corpus (2)

• Spontaneous Lorentz and Diffeomorphism Violation, Massive Modes, and Gravity
• Vector models of gravitational Lorentz symmetry breaking

Cited by in corpus (4)

• 3+1 Formulation of the Standard-Model Extension Gravity Sector
• Spontaneous symmetry breaking in models with second-class constraints
• Bumblebee gravity: spherically-symmetric solutions away from the potential minimum
• Singular Hamiltonians in models with spontaneous Lorentz symmetry breaking