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Nonlinear sigma models with non-compact target space and non-amen-able symmetry group were introduced long ago in the study of disor-dered electron systems. They also occur in dimensionally reduced qu...
Nonlinear sigma models with non-compact target space and non-amen-able symmetry group were introduced long ago in the study of disor-dered electron systems.
Do the Ricci and energy-momentum tensors have "duality'' in the context of their Lie symmetries?
Ricci energy-momentum tensors
2010/12/20
The Ricci and energy-momentum tensors have the same algebraic sym-metries. In the Einstein equations they look “dual” to each other, in that interchang-ing them and inverting the gravitational couplin...
Symmetries, Stability, and Control in Nonlinear Systems and Networks
Nonlinear Systems Networks math
2010/11/8
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and eq...
Discretizations of continuum theories often do not preserve the gauge symmetry content.This occurs in particular for diffeomorphism symmetry in general relativity, which leads to severe difficulties b...
Nonlinear sigma models with non-compact target space and non-amen-able symmetry group were introduced long ago in the study of disordered electron systems. They also occur in dimensionally reduced qu...
Symmetries of Self-Dual Yang-Mills Equations Dimensionally Reduced From (2,2) Space-time
Self-Dual Yang-Mills Equations Space-time
2010/12/22
We construct infinite-dimensional symmetries of the two dimensional equation which results from the dimensional reduction of the self-duality condition in (2, 2) signature space-time. These are symme...
On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory
Symmetries Conservation laws Noether theorem Hamiltonian field theories
2010/12/6
This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian
systems in first-order classical field theories. Thus, we introduce a particular class of
symmetries and s...
Fluctuations arise universally in Nature as a re ection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, uctuations encode fundamental aspects of the ph...
While modern optics is largely a physics of harmonic oscillators and two-by-two matrices, it is possible to learn about some hidden properties of the two-by-two matrix from optical systems.
Internal Space-time Symmetries of Particles derivable from Periodic Systems in Optics
Internal Space-time Symmetries Particles derivable Periodic Systems in Optics
2010/10/27
While modern optics is largely a physics of harmonic oscillators and two-by-two matrices, it is possible to learn about some hidden properties of the two-by-two matrix from optical systems. Since two-...
Symmetries for the Ablowitz-Ladik hierarchy: II. Integrable discrete nonlinear Schrödinger equation and discrete AKNS hierarchy
Ablowitz-Ladik hierarchy nonlinear Schrö dinger equation discrete AKNS hierarchy
2010/4/21
In the paper we continue to consider symmetries related to the Ablowitz-Ladik hierarchy. We derive symmetries for the integrable discrete nonlinear Schr\"odinger hierarchy and discrete AKNS hierarchy....
Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations
gravity Chern–Simons theory deformation spacetime anti-de Sitter hyperbolic cosmological constant contraction
2010/3/18
We show how the constant curvature spacetimes of 3d gravity and the associated symmetry algebras can be derived from a single quantum deformation of the 3d Lorentz algebra sl(2,R). We investigate the ...
Noether Symmetries and Covariant Conservation Laws in Classical, Relativistic and Quantum Physics
Noether Symmetries Quantum Physics Covariant Conservation Laws
2010/3/18
We review the Lagrangian formulation of Noether symmetries (as well as "generalized Noether symmetries") in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-calle...
Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method
conservation laws quad-graph equations
2010/4/1
The application of the Gardner method for generation of conservation laws to all the ABS equations is considered. It is shown that all the necessary information for the application of the Gardner meth...