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Michael D. Seifert

Publications and source records attributed to Michael D. Seifert.

12 recordsLinked to original sources
arXiv2019

Singular Hamiltonians in models with spontaneous Lorentz symmetry breaking

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.

hep-th↗
arXiv2018

Constraints and degrees of freedom in Lorentz-violating field theories

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.

hep-th↗
arXiv2014

Lorentz violation and topological defects

If Lorentz symmetry is broken, it must have occurred dynamically, via a vector or tensor field whose potential energy forces it to take on a non-zero background expectation value "in vacuum". If the set of minima of this potential (the vacuum manifold) has a non-trivial topology, then there can arise topological defects: stable solutions in which the field approaches different potential minima as we go to infinity in different directions. I discuss the current status of research into these topological defects in the context of Lorentz symmetry breaking, including recent results concerning the birefringent light-bending of monopole solutions, and the search for models supporting cosmic-string and domain-wall defects.

hep-th↗
arXiv2013

Direct-coupling lensing by antisymmetric tensor monopoles

We discuss the effects of a direct coupling between a rank-two antisymmetric tensor field and the Maxwell field. The coupling we consider leads to vacuum birefringence, allowing us to place constraints on the magnitude of the tensor field and the strength of its coupling to the Maxwell field via cosmological birefringence measurements. For light propagating in the presence of a topological defect solution, we find that light rays with different polarizations will follow different trajectories; the magnitude of this deflection is predicted to be extremely small (on the order of 10^-10 arcseconds). We discuss the plausibility of this phenomenon as a method for detection of these monopoles, along with the applicability of our methods to other possible couplings between the tensor field and the Maxwell field.

hep-th↗
arXiv2010

Dynamical Lorentz symmetry breaking and topological defects

I discuss the possibility of topological defect solutions in field theories containing a tensor field which spontaneously breaks Lorentz symmetry. I find that for theories of a tensor with rank r <= 5 and for which the vacuum manifold consists of the tensors whose "square" is some constant value, only three types of tensor (vectors, antisymmetric two-tensors, and symmetric two-tensors) have the appropriate vacuum manifold topology to support topological defects. Of these, topological defect solutions can be easily constructed for two: vector domain wall solutions and antisymmetric tensor monopole solutions. These antisymmetric tensor monopole solutions are in principle detectible via their gravitational lensing effects.

hep-th↗
arXiv2010

Generalized bumblebee models and Lorentz-violating electrodynamics

The breaking of Lorentz symmetry via a dynamical mechanism, with a tensor field which takes on a non-zero expectation value in vacuum, has been a subject of significant research activity in recent years. In certain models of this type, the perturbations of the "Lorentz-violating field" about this background may be identified with known forces. I present the results of applying this interpretation to the "generalized bumblebee models" found in a prior work. In this model, the perturbations of a Lorentz-violating vector field can be interpreted as a photon field. However, the speed of propagation of this "bumblebee photon" is direction-dependent and differs from the limiting speed of conventional matter, leading to measurable physical effects. Bounds on the parameters of this theory can then be derived from resonator experiments, accelerator physics, and cosmic ray observations.

hep-ph↗
arXiv2009

Vector models of gravitational Lorentz symmetry breaking

Spontaneous Lorentz symmetry breaking can occur when the dynamics of a tensor field cause it to take on a non-zero expectation value in vacuo, thereby providing one or more "preferred directions" in spacetime. Couplings between such fields and spacetime curvature will then affect the dynamics of the metric, leading to interesting gravitational effects. Bailey & Kostelecky developed a post-Newtonian formalism that, under certain conditions concerning the field's couplings and stress-energy, allows for the analysis of gravitational effects in the presence of Lorentz symmetry breaking. We perform a systematic survey of vector models of spontaneous Lorentz symmetry breaking. We find that a two-parameter class of vector models, those with kinetic terms we call "pseudo-Maxwell," can be successfully analyzed under the Bailey-Kostelecky formalism, and that one of these two "dimensions" in parameter space has not yet been explored as a possible mechanism of spontaneous Lorentz symmetry breaking.

gr-qc↗
arXiv2007

Stability of spherically symmetric solutions in modified theories of gravity

In recent years, a number of alternative theories of gravity have been proposed as possible resolutions of certain cosmological problems or as toy models for possible but heretofore unobserved effects. However, the implications of such theories for the stability of structures such as stars have not been fully investigated. We use our "generalized variational principle", described in a previous work, to analyze the stability of static spherically symmetric solutions to spherically symmetric perturbations in three such alternative theories: Carroll et al.'s f(R) gravity, Jacobson & Mattingly's "Einstein-aether theory", and Bekenstein's TeVeS. We find that in the presence of matter, f(R) gravity is highly unstable; that the stability conditions for spherically symmetric curved vacuum Einstein-aether backgrounds are the same as those for linearized stability about flat spacetime, with one exceptional case; and that the "kinetic terms" of vacuum TeVeS are indefinite in a curved background, leading to an instability.

gr-qc↗
arXiv2007

A general variational principle for spherically symmetric perturbations in diffeomorphism covariant theories

We present a general method for the analysis of the stability of static, spherically symmetric solutions to spherically symmetric perturbations in an arbitrary diffeomorphism covariant Lagrangian field theory. Our method involves fixing the gauge and solving the linearized gravitational field equations to eliminate the metric perturbation variable in terms of the matter variables. In a wide class of cases--which include f(R) gravity, the Einstein-aether theory of Jacobson and Mattingly, and Bekenstein's TeVeS theory--the remaining perturbation equations for the matter fields are second order in time. We show how the symplectic current arising from the original Lagrangian gives rise to a symmetric bilinear form on the variables of the reduced theory. If this bilinear form is positive definite, it provides an inner product that puts the equations of motion of the reduced theory into a self-adjoint form. A variational principle can then be written down immediately, from which stability can be tested readily. We illustrate our method in the case of Einstein's equation with perfect fluid matter, thereby re-deriving, in a systematic manner, Chandrasekhar's variational principle for radial oscillations of spherically symmetric stars. In a subsequent paper, we will apply our analysis to f(R) gravity, the Einstein-aether theory, and Bekenstein's TeVeS theory.

gr-qc↗
arXiv2001

Modelling Space with an Atom of Quantum Geometry

Within the context of loop quantum gravity there are several operators which measure geometry quantities. This work examines two of these operators, volume and angle, to study quantum geometry at a single spin network vertex - ``an atom of geometry.'' Several aspects of the angle operator are examined in detail including minimum angles, level spacing, and the distribution of angles. The high spin limit of the volume operator is also studied for monochromatic vertices. The results show that demands of the correct scaling relations between area and volume and requirements of the expected behavior of angles in three dimensional flat space require high-valence vertices with total spins of approximately 10^20.

gr-qc↗