相关论文: Schr\"odinger symmetry: a historical review

Schr\"odinger symmetry emerged in a ``fluid limit" from a full superspace to several mini-superspace models. We consider two spherically-symmetric static mini-superspace models with matter fields and verify the robustness of this emergent…

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…

One of the important extensions of Riemann geometry is Weyl geometry, which is essentially based on the ideas of conformal invariance and nonmetricity. A similar non-Riemannian geometry was proposed by Erwin Schr\"{o}dinger in the late…

The non-relativistic conformal symmetry found by Jackiw and Pi for the coupled Chern-Simons and gauged nonlinear Schr\"odinger equations in the plane is derived in a non-relativistic Kaluza-Klein framework.

The set of dynamic symmetries of the scalar free Schr\"odinger equation in d space dimensions gives a realization of the Schr\"odinger algebra that may be extended into a representation of the conformal algebra in d+2 dimensions, which…

The Poincar\'e symmetry can be contracted in two ways to yield the Galilei symmetry and the Carroll symmetry. The well-known Schr\"odinger equation exhibits the Galilei symmetry and is a fundamental equation in Galilean quantum mechanics.…

We determine the Lie point symmetries of the Schr\"{o}dinger and the Klein Gordon equations in a general Riemannian space. It is shown that these symmetries are related with the homothetic and the conformal algebra of the metric of the…

We discuss non-relativistic conformal algebras generalizing the Schr\"odinger algebra. One instance of these algebras is a conformal, acceleration-extended, Galilei algebra, which arises also as a contraction of the relativistic conformal…

Non-relativistic conformal (''Schr\"odinger'') symmetry is derived in a Kaluza-Klein type framework. Lightlike reduction of the massless Dirac equation from 5D Minkowski space yields L\'evy-Leblond's non-relativistic equation for a spin 1/2…

We present a unified framework for the rigorous derivation of conservation laws and related identities for nonlinear Schr\"odinger equations with power-type nonlinearities. This approach treats the equation in its Duhamel form and uses the…

The last multiplier of Jacobi provides a route for the determination of families of Lagrangians for a given system. We show that the members of a family are equivalent in that they differ by a total time derivative. We derive the…

This article provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei…

We investigate precise structural relations between the standard Schr\"odinger equation and its Carrollian analogue-the Carroll-Schr\"odinger equation-in 1+1 dimensions, with emphasis on dualities, potential maps, and solution behavior. Our…

The free Schr\"odinger equation with mass M can be turned into a non-massive Klein-Gordon equation via Fourier transformation with respect to M. The kinematic symmetry algebra sch_d of the free d-dimensional Schr\"odinger equation with M…

Using numerical techniques, we study the collapse of a scalar field configuration in the Newtonian limit of the spherically symmetric Einstein--Klein--Gordon (EKG) system, which results in the so called Schr\"odinger--Newton (SN) set of…

Schr\"odinger connections are a special class of affine connections, which despite being metric incompatible, preserve length of vectors under autoparallel transport. In the present paper, we introduce a novel coordinate-free formulation of…

We are describing relations between Schr\"odinger's variational problem and Onsager's approach to nonequilibrium statistical mechanics. Although the second work on reciprocal relations and detailed balance has been published in the same…

In the class of metrics of a generic conformal structure there exists a distinguishing metric. This was noticed by Albert Einstein in a lesser-known paper of 1921 (Berl. Ber., 1921, pp. 261-264). We explore this finding from a geometrical…

We prove that the simplest gravitational symmetry reduced models describing cosmology and black holes mechanics are invariant under the Schr\"{o}dinger group. We consider the flat FRW cosmology filled with a massless scalar field and the…

The covariance of the Schr\"odinger equation under Galilei boosts and the compatibility of nonrelativistic quantum mechanics with Einstein's equivalence principle have been constrained for so long to the existence of a superselection rule…