Related papers: Schr\"odinger Manifolds
We provide a Lie algebra expansion procedure to construct three-dimensional higher-order Schr\"odinger algebras which relies on a particular subalgebra of the four-dimensional relativistic conformal algebra. In particular, we reproduce the…
Using variational considerations, we establish that there exists a new symmetric trace-free tensor conformal invariant of hypersurfaces embeddings in even dimensional conformal manifolds. This conformal invariant completes the family of…
The simplices and the complexes arsing form the grading of the fundamental (desymmetrized) domain of arithmetical groups and non-arithmetical groups, as well as their extended (symmetrized) ones are described also for oriented manifolds in…
In this paper, we prove a rigidity theorem for Poincar\'e-Einstein manifolds whose conformal infinity is a flat Euclidean space. The proof relies on analyzing the propagation of curvature tensors over the level sets of an adapted boundary…
We construct explicit examples of non-relativistic supersymmetric field theories on curved Newton-Cartan three-manifolds. These results are obtained by performing a null reduction of four-dimensional supersymmetric field theories on…
Perhaps the fundamental theorem of geometric group theory, the Milnor--Schwarz lemma gives conditions under which the orbit map relating the geometry of a geodesic metric space and the word metric on a group acting isometrically on the…
Motivated by questions about $\mathbb{C}_p$-valued Fourier transform on the locally compact group $(\mathbb{Q}_p^d,+)$, we study invariant norms on the $p$-adic Schr\"odinger representation of the Heisenberg group. Our main result is a…
Bound and scattering state Schr\"odinger functions of nonrelativistic quantum mechanics as representation matrix elements of space and time are embedded into residual representations of spacetime as generalizations of Feynman propagators.…
We construct, using the supersymplectic framework of Berezin, Kostant and others, two types of supersymmetric extensions of the Schr\"odinger algebra (itself a conformal extension of the Galilei algebra). An `$I$-type' extension exists in…
We present a definition of null G-structures on Lorentzian manifolds and investigate their geometric properties. This definition includes the Robinson structure on 4-dimensional black holes as well as the null structures that appear in all…
We investigate how the Lax-Novikov integral in the perfectly invisible $PT$-regularized zero-gap quantum conformal and superconformal mechanics systems affects on their (super)-conformal symmetries. We show that the expansion of the…
We give a review of some group-theoretical results related to non-relativistic holography. Our main playgrounds are the Schr\"odinger equation and the Schr\"odinger algebra. We first recall the interpretation of non-relativistic holography…
Conformal Carrollian groups are known to be isomorphic to Bondi-Metzner-Sachs (BMS) groups that arise as the asymptotic symmetries at the null boundary of Minkowski spacetime. The Carrollian algebra is obtained from the Poincare algebra by…
We establish sharp-in-time kernel and dispersive estimates for the Schr\"odinger equation on non-compact Riemannian symmetric spaces of any rank. Due to the particular geometry at infinity and the Kunze-Stein phenomenon, these properties…
In this work, we extend the time-dependent conformable Schr\"odinger equation for a fractional dimensional system of N spatial coordinates to be used as an effective description of anisotropic and confined systems. A specific example is…
We study non-linear Schr\"odinger operators on graphs. We construct minimal nonnegative solutions to corresponding semi-linear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a non-linear…
Using recent results on string on $AdS_{3}\times N^d$, where N is a d-dimensional compact manifold, we re-examine the derivation of the non trivial extension of the (1+2) dimensional-Poincar\'e algebra obtained by Rausch de Traubenberg and…
In this article we characterize the extreme points of the unit ball of a non-commutative (quantum) Lorentz space associated with a semi-finite von Neumann algebra. This enables us to show that surjective isometries between non-commutative…
The book contains a collection of works on Riemann-Cartan and metric-affine manifolds provided with nonlinear connection structure and on generalized Finsler-Lagrange and Cartan-Hamilton geometries and Clifford structures modelled on such…
We present the geometry of spacetimes that are tangentially approximated by de Sitter spaces whose cosmological constants vary over spacetime. Cartan geometry provides one with the tools to describe manifolds that reduce to a homogeneous…