Search results for "nonlinear"
showing 10 items of 3684 documents
The Schouten - Nijenhuis bracket, cohomology and generalized Poisson structures
1996
Newly introduced generalized Poisson structures based on suitable skew-symmetric contravariant tensors of even order are discussed in terms of the Schouten-Nijenhuis bracket. The associated `Jacobi identities' are expressed as conditions on these tensors, the cohomological contents of which is given. In particular, we determine the linear generalized Poisson structures which can be constructed on the dual spaces of simple Lie algebras.
Finite size spectrum of SU(N) principal chiral field from discrete Hirota dynamics
2016
Using recently proposed method of discrete Hirota dynamics for integrable (1+1)D quantum field theories on a finite space circle of length L, we derive and test numerically a finite system of nonlinear integral equations for the exact spectrum of energies of SU(N)xSU(N) principal chiral field model as functions of m L, where m is the mass scale. We propose a determinant solution of the underlying Y-system, or Hirota equation, in terms of determinants (Wronskians) of NxN matrices parameterized by N-1 functions of the spectral parameter, with the known analytical properties at finite L. Although the method works in principle for any state, the explicit equations are written for states in the …
Small and hollow magnetic monopoles
2018
We deal with the presence of magnetic monopoles in a non Abelian model that generalizes the standard 't~Hooft-Polyakov model in three spatial dimensions. We investigate the energy density of the static and spherically symmetric solutions to find first order differential equations that solve the equations of motion. The system is further studied and two distinct classes of solutions are obtained, one that can also be described by analytical solutions which is called small monopole, since it is significantly smaller than the standard 't~Hooft-Polyakov monopole. The other type of structure is the hollow monopole, since the energy density is endowed with a hole at its core. The hollow monopole …
DEFORMATION QUANTIZATION OF COADJOINT ORBITS
2000
A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.
Nonlinear σ -models in the Eddington-inspired Born-Infeld gravity
2020
In this paper we consider two different nonlinear $\sigma$-models minimally coupled to Eddington-inspired Born-Infeld gravity. We show that the resultant geometries represent minimal modifications with respect to those found in GR, though with important physical consequences. In particular, wormhole structures always arise, though this does not guarantee by itself the geodesic completeness of those space-times. In one of the models, quadratic in the canonical kinetic term, we identify a subset of solutions which are regular everywhere and are geodesically complete. We discuss characteristic features of these solutions and their dependence on the relationship between mass and global charge.
The Gravity Lagrangian According to Solar System Experiments
2005
In this work we show that the gravity lagrangian f(R) at relatively low curvatures in both metric and Palatini formalisms is a bounded function that can only depart from the linearity within the limits defined by well known functions. We obtain those functions by analysing a set of inequalities that any f(R) theory must satisfy in order to be compatible with laboratory and solar system observational constraints. This result implies that the recently suggested f(R) gravity theories with nonlinear terms that dominate at low curvatures are incompatible with observations and, therefore, cannot represent a valid mechanism to justify the cosmic speed-up.
Quantum deformation of the Poincare supergroup and kappa -deformed superspace
1994
The classical $r$-matrix for $N=1$ superPoincar{\'e} algebra, given by Lukierski, Nowicki and Sobczyk is used to describe the graded Poisson structure on the $N=1$ Poincar{\'e} supergroup. The standard correspondence principle between the even (odd) Poisson brackets and (anti)commutators leads to the consistent quantum deformation of the superPoincar{\'e} group with the deformation parameter $q$ described by fundamental mass parameter $\kappa \quad (\kappa^{-1}=\ln{q})$. The $\kappa$-deformation of $N=1$ superspace as dual to the $\kappa$-deformed supersymmetry algebra is discussed.
Hopf algebras, renormalization and noncommutative geometry
1998
We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of transverse index theory for foliations.
Abelian current algebra and the Virasoro algebra on the lattice
1993
We describe how a natural lattice analogue of the abelian current algebra combined with free discrete time dynamics gives rise to the lattice Virasoro algebra and corresponding hierarchy of conservation laws.
Supersymmetry in non commutative superspaces
2003
Non commutative superspaces can be introduced as the Moyal-Weyl quantization of a Poisson bracket for classical superfields. Different deformations are studied corresponding to constant background fields in string theory. Supersymmetric and non supersymmetric deformations can be defined, depending on the differential operators used to define the Poisson bracket. Some examples of deformed, 4 dimensional lagrangians are given. For extended superspace (N>1), some new deformations can be defined, with no analogue in the N=1 case.