Related papers: Lorentz Violation in a Diffeomorphism-Invariant Th…
Remnant low-energy effects of Planck-scale Lorentz breaking in candidate fundamental theories typically include modified one-particle dispersion relations. Theoretical constraints on such modifications are discussed leading to the exclusion…
In this work, we investigate a theory of linear Weyl gravity coupled to a scalar field and study the scenario in which Lorentz symmetry is broken by a non-vanishing vacuum expectation value of the Weyl field in the flat space limit after…
Translational invariance requires that physical predictions are independent of the choice of spatial coordinate system used. The time dilatation effect of special relativity is shown to manifestly respect this invariance. Consideration of…
A short review is given of some theoretical approaches to CPT violation. A potentially realistic possibility is that small apparent breaking of CPT and Lorentz symmetry could arise at the level of the standard model from spontaneous…
In this letter we reconsider the role of Lorentz invariance in the dynamical generation of the observed internal symmetries. We argue that, generally, Lorentz invariance can only be imposed in the sense that all Lorentz non-invariant…
The interpretation of neutrino oscillation data has led to the question whether, in principle, an antiparticle like antineutrino can have a different mass than its particle. In the framework of a Lorentz invariant CPT violation, which is…
The concept of $Diff^4$ invariant Poincare transformations is a cornerstone of T(opological) G(eometro)D(ynamics). This concept makes it possible to understand the concept of subjective time and irreversibelity as well as nontriviality of…
If one modifies the Dirac equation in momentum space to $[\gamma^{\mu}p_{\mu}-m-\Delta m(\theta(p_{0})-\theta(-p_{0})) \theta(p_{\mu}^{2})]\psi(p)=0$, the symmetry of positive and negative energy eigenvalues is lifted by $m\pm \Delta m$ for…
Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…
Symmetry breaking in two-dimensional layered materials plays a significant role in their macroscopic electrical, optical, magnetic and topological properties, including but not limited to spin-polarization effects, valley-contrasting…
We study the symmetry breaking phenomenon for an elliptic equation involving the fractional Laplacian in a large ball. Our main tool is an extension of the Strauss radial lemma involving the fractional Laplacian, which might be of…
Conceptual difficulties in semiclassical and quantum gravity arise from diffeomorphism invariance of classical general relativity. With a motivation to shed some light on these difficulties, we study a class of toy models for which…
We revisit one of the earliest proposals for deformed dispersion relations in the light of recent results on dynamical dimensional reduction and production of cosmological fluctuations. Depending on the specification of the measure of…
Recent claims point out that possible violations of Lorentz symmetry appearing in some semiclassical models of extended matter dynamics motivated by loop quantum gravity can be removed by a different choice of canonically conjugated…
We study coordinate-invariance of some asymptotic invariants such as the ADM mass or the Chru\'sciel-Herzlich momentum, given by an integral over a "boundary at infinity". When changing the coordinates at infinity, some terms in the change…
We study the effects of Lorentz symmetry violation on the scalar CMBR bispectrum. Our quantitative results show that there can be enhancements in the bispectrum for specific configurations in momentum space, when the modified dispersion…
Symmetry breaking is reported for continuous families of solitons in the nonlinear Schr\"odinger equation with a two-dimensional complex potential. This symmetry-breaking bifurcation is forbidden in generic complex potentials. However, for…
For a field theory that is invariant under diffeomorphisms there is a subtle interplay between symmetries, conservation laws and the phase space of the theory. The natural language for describing these ideas is that of differential forms…
We define a bordism invariant for the fiberwise intersection theory. Under some certain conditions, this invariant is an obstruction for the theory.
Lorentz invariance is such a basic principle in fundamental physics that it must be constantly tested and that any proposal of its violation and breakdown of CPT symmetry, that might characterize some approaches to quantum gravity, should…