Related papers: Discreteness without symmetry breaking: a theorem
Motivated by the severity of the bounds on Lorentz violation in the presence of ordinary gravity, we study frameworks in which Lorentz violation does not affect the spacetime geometry. We show that there are at least two inequivalent…
The following four statements have been proven decades ago already, but they continue to induce a strange feeling: - All curvature invariants of a gravitational wave vanish - in spite of the fact that it represents a nonflat spacetime. -…
The soft photon and soft graviton theorems of Weinberg are known to derive from conservation laws associated with asymptotic symmetries. Within the corresponding classical theories, one often speaks of spontaneous symmetry breaking and…
We study potentially observable consequences of spatiotemporal discreteness for the motion of massive and massless particles. First we describe some simple intrinsic models for the motion of a massive point particle in a fixed causal set…
Sampling theory is a discipline in communications engineering involved with the exact reconstruction of continuous signals from discrete sets of sample points. From a physics perspective, this is interesting in relation to the question of…
According to the Weinstein splitting theorem, any Poisson manifold is locally, near any given point, a product of a symplectic manifold with another Poisson manifold whose Poisson structure vanishes at the point. Similar splitting results…
The Lorentz symmetry and the space and time translational symmetry are fundamental symmetries of nature. Crystals are the manifestation of the continuous space translational symmetry being spontaneously broken into a discrete one. We argue…
We investigate the analytic structure of scattering amplitudes in theories in which Lorentz invariance is spontaneously broken. We do so by computing and studying the S-matrix for a simple example: a superfluid described by a complex scalar…
Entanglement entropy in causal sets offers a fundamentally covariant characterisation of quantum field degrees of freedom. A known result in this context is that the degrees of freedom consist of a number of contributions that have…
Gravitational waves from merging compact objects provides the opportunity to explore the properties of black holes and neutron stars in the strong regime of gravity. It is therefore of interest to explore the theoretical model that…
In the special theory of relativity, Lorentz invariance is extended in Minkowski spacetime from ideal inertial observers to actual observers by means of the hypothesis of locality, which postulates that accelerated observers are always…
The causal set approach to quantum gravity models spacetime as a discrete structure - a causal set. Recent research has led to causal set models for the retarded propagator for the Klein-Gordon equation and the d'Alembertian operator. These…
Motivated by generalized uncertainty principle, we derive a discrete picture of the space that respects Lorentz symmetry as well as gauge symmetry through setting an equivalency between linear GUP correction term and electromagnetic…
The causal set action of dimension $d$ is investigated for causal sets that are Poisson sprinklings into submanifolds of $d$-dimensional Minkowski space. Evidence, both analytic and numerical, is provided for the conjecture that the mean of…
Without Lorentz invariance, spontaneous global symmetry breaking can lead to multicritical Nambu-Goldstone modes with a higher-order low-energy dispersion $\omega\sim k^n$ ($n=2,3,\ldots$), whose naturalness is protected by polynomial shift…
I analyze the deformation of Lorentz symmetry that holds in certain noncommutative spacetimes and the way in which Lorentz symmetry is broken in other noncommutative spacetimes. I also observe that discretization of areas does not…
A new way of supersymmetry breaking involving a dynamical parameter is introduced. It is independent of particle phenomenology and gauge groups. The only requirement is that Lorentz invariance be valid strictly infinitesimally (i. e.…
We demonstrate that point-like defects in non-collinear magnets give rise to a highly dispersive structure in the magnon scattering, violating a standard paradigm of its momentum independence. For a single impurity spin coupled to a…
In this brief, and by no means complete, review I discuss situations in string theory, in which Lorentz Invariance Violation may occur in a way consistent with world-sheet conformal invariance, thereby leading to acceptable, in principle,…
We consider the scattering of waves by a penetrable inclusion embedded in some reference medium. We exhibit examples of materials and geometries for which non-scattering frequencies exist, i.e., for which at some frequencies there are…