Related papers: Disformal transformation in Newton-Cartan geometry
We re-formulate the notion of a Newton-Cartan manifold and clarify the compatibility conditions of a connection with torsion with the Newton-Cartan structure.
The conformal transformations corresponding to $N$-Galilean conformal symmetries, previously defined as canonical symmetry transformations on phase space, are constructed as point transformations in coordinate space.
A motivation of using noncommutative and nonarchimedean geometry on very short distances is given. Besides some mathematical preliminaries, we give a short introduction in adelic quantum mechanics. We also recall to basic ideas and tools…
We formulate a geometric framework that allows to study momentum and energy transport in non-relativistic systems. It amounts to coupling of the non-relativistic system to the Newton-Cartan geometry with torsion. The approach generalizes…
This paper studies hamiltonization of nonholonomic systems using geometric tools. By making use of symmetries and suitable first integrals of the system, we explicitly define a global 2-form for which the gauge transformed nonholonomic…
Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as…
We review aspects of our formalism for differential geometry on noncommutative and nonassociative spaces which arise from cochain twist deformation quantization of manifolds. We work in the simplest setting of trivial vector bundles and…
Using Cartan's equivalence method for point transformations we obtain from first principles the conformal geometry associated with third order ODEs and a special class of PDEs in two dimensions. We explicitly construct the null tetrads of a…
We define Radon transform and its inverse on the two-dimensional anti-de Sitter space over local fields using a novel construction through a quadratic equation over the local field. We show that the holographic bulk reconstruction of…
A quantization over a manifold can be seen as a way to construct a differential operator with prescribed principal symbol. The quantization map is moreover required to be a linear bijection. It is known that there is in general no natural…
We study disformal transformations of the metric in the cosmological context. We first consider the disformal transformation generated by a scalar field $\phi$ and show that the curvature and tensor perturbations on the uniform $\phi$…
We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The…
We give uniqueness theorem and reconstruction algorithm for the nonlinearized problem of finding the dielectric anisotropy f of the medium from non-overdetermined polarization tomography data. We assume that the medium has uniform…
We study a non-relativistic limit of 11-dimensional supergravity. This limit leads to a theory with an underlying membrane Newton-Cartan geometry. Consistency of the non-relativistic limit requires the imposition of constraints, requiring…
The Horndeski action is the most general one involving a metric and a scalar field that leads to second-order field equations in four dimensions. Being the natural extension of the well-known scalar-tensor theories, its structure and…
In this paper, we study the differential geometry of null Cartan curves under the similarity transformations in the Minkowski space-time. Besides, we extend the fundamental theorem for a null Cartan curve according to a similarity motion.…
The 1+3 covariant approach and the covariant gauge-invariant approach to perturbations are used to analyze in depth conformal transformations in cosmology. Such techniques allow us to obtain very interesting insights on the physical content…
The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an…
Invertible disformal transformations are a useful tool to investigate ghost-free scalar-tensor theories. By performing a higher-derivative generalization of the invertible disformal transformation on Horndeski theories, we construct a novel…
We revisit the light or heat-induced changes in topography of initially flat sheets of solid that elongate or contract along patterned, in-plane director fields. For radial or azimuthal directors, negative Gaussian curvature is generated --…