相关论文: The Hyperbolic Heisenberg and Sigma Models in (1+1…
Motivated by recent work on integrable flows of curves and 1+1 dimensional sigma models, several O(N)-invariant classes of hyperbolic equations $u_{tx} =f(u,u_t,u_x)$ for an $N$-component vector $u(t,x)$ are considered. In each class we…
This paper concentrates on the Heisenberg ferromagnetic spin chain (HFSC) equation in (2+1)-dimensions modelling nonlinear wave propagation in ferromagnetic spin chain. A variable transformation is first employed to reduce the studied…
Symmetric hyperbolic systems of equations are explicitly constructed for a general class of tensor fields by considering their structure as r-fold forms. The hyperbolizations depend on 2r-1 arbitrary timelike vectors. The importance of the…
We consider the $ U(1) $ sigma model in the two dimensional space-time which is a field-theoretical model possessing a nontrivial topology. It is pointed out that its topological structure is characterized by the zero-mode and the winding…
By using the prolongation structure theory proposed by Morris, we give a (2+1)-dimensional integrable inhomogeneous Heisenberg Ferromagnet models, namely, the inhomogeneous Myrzakulov I equation. Through the motion of space curves endowed…
While many integrable spin systems are known to exist in (1+1) and (2+1) dimensions, the integrability property of the physically important (2+1) dimensional isotropic Heisenberg ferromagnetic spin system in the continuum limit has not been…
In this paper we introduce topological modules over the ring of bihyperbolic numbers. We discuss bihyperbolic convexity, bihyperbolic-valued seminorms and bihyperbolic-valued Minkowski functionals in topological bihyperbolic modules.…
In its most general formulation a quantum kinematical system is described by a Heisenberg group; the "configuration space" in this case corresponds to a maximal isotropic subgroup. We study irreducible models for Heisenberg groups based on…
This paper contains an analysis of rank-k solutions in terms of Riemann invariants, obtained from interrelations between two concepts, that of the symmetry reduction method and of the generalized method of characteristics for first order…
The energy structure and the thermodynamics of ferrimagnetic Heisenberg chains of alternating spins S and s are described in terms of the Schwinger bosons and modified spin waves. In the Schwinger representation, we average the local…
A multidimensional gravitational model containing scalar fields and antisymmetric forms is considered. The manifold is chosen in the form $M = M_0 \times M_1 \times \cdots \times M_n$, where $M_i$ are Einstein spaces ($i \geq 1$). The…
We analyze two extended versions [the Ishimori model (IM) and a related system, which will be called modified Ishimori model (mIM)] of the continuous Heisenberg model in (2+1)-dimensions within the complex Hirota scheme. The IM, proposed in…
We analyze solutions of string theory and supergravity which involve real hyperbolic spaces. Examples of string compactifications are given in terms of hyperbolic coset spaces of finite volume $\Gamma\backslash {\mathbb H}^N$, where…
The nature of space-time at high energy is an open question and the link between extra-dimensional theories with the physics of the Standard Model can not be established in a unique way. The compactification path is not unique and…
Starting from the geometrical interpretation of integrable vortices on two-dimensional hyperbolic space as conical singularities, we explain how this picture can be expressed in the language of Cartan connections, and how it can be lifted…
In this paper we classify all 4+1 cosmological models where the spatial hypersurfaces are connected and simply connected homogeneous Riemannian manifolds. These models come in two categories, multiply transitive and simply transitive…
It is known that there exist an infinite number of inequivalent quantizations on a topologically nontrivial manifold even if it is a finite-dimensional manifold. In this paper we consider the abelian sigma model in (1+1) dimensions to…
Rigidly superconformal sigma models in higher than two dimensions are constructed. These models rely on the existence of conformal Killing spinors on the $p+1$ dimensional worldvolume $(p\le 5)$, and homothetic conformal Killing vectors in…
The correlated fermionic many-particle system, near infinite scattering length, reveals an underlying Heisenberg symmetry in one dimension, as compared to an $SO(2,1)$ symmetry in two dimensions. This facilitates an exact map from the…
The abelian sigma model in (1+1) dimensions is a field theoretical model which has a field $ \phi : S^1 \to S^1 $. An algebra of the quantum field is defined respecting the topological aspect of the model. It is shown that the zero-mode has…