Related papers: Weyl Invariant Dynamics in 3 Dimensions

In [1], we have presented the theoretical background for finding the Elementary Invariants for a 3D system of first order rational differential equations (1ODEs). We have also provided an algorithm to find such Invariants. Here we introduce…

Using the method of moving frames we analyze the algebra of differential invariants for surfaces in three-dimensional affine geometry. For elliptic, hyperbolic, and parabolic points, we show that if the algebra of differential invariants is…

We introduce a class of dynamical systems having an invariant measure, the modifications of well known systems on Lie groups: LR and L+R systems. As an example, we study modified Veselova nonholonomic rigid body problem, considered as a…

In the first part of this work the classical and statistical aspects of the dynamics of an inextensible chain in three dimensions are investigated. In the second part the special case of a chain admitting only fixed angles with respect to…

Following the realization of Weyl semimetals in quantum electronic materials, classical wave analogues of Weyl materials have also been theorized and experimentally demonstrated in photonics and acoustics. Weyl points in elastic systems,…

An algorithm to obtain the Weyl anomaly in higher dimensions is presented. It is based on the heat-kernel method. Feynman rules, such as the vertex rule and the propagator rule, are given in (regularized) coordinate space. Graphical…

We construct new families of conformally invariant differential operators acting on densities. We introduce a simple, direct approach which shows that all such operators arise via this construction when the degree is bounded by the…

It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…

In this paper give a survey about L^2-invariants focusing on 3-manifolds.

Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…

Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.

We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.

We demonstrate a few unique dynamical properties of point-gap Weyl semimetal, an intrinsic non-Hermitian topological phase in three dimensions. We consider a concrete model where a pair of Weyl points reside on the imaginary axis of the…

We demonstrate the ``peeling property'' of the Weyl tensor in higher dimensions in the case of even dimensions (and with some additional assumptions), thereby providing a first step towards understanding of the general peeling behaviour of…

A new version of hidden variables theory founded on the generalisation of world's geometry is proposed. The quantum-mechanical motion as the motion in some "inner space", which has a structure of the integrable Weyl space is examined.…

We give a description of the cohomological invariants mod 2 of a Weyl group G in terms of the involution classes of G.

A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the…

We consider local geometry of sub-pseudo-Riemannian structures on contact manifolds. We construct fundamental invariants of the structures and show that the structures give rise to Einstein-Weyl geometries in dimension 3, provided that…

We survey several generalizations of the Weyl algebra including generalized Weyl algebras, twisted generalized Weyl algebras, quantized Weyl algebras, and Bell-Rogalski algebras. Attention is paid to ring-theoretic properties,…

Applications of the three-dimensional transformation for rotating coordinate systems to quantum mechanics, general theory relativity and optics are considered.