In this paper an extension of the q-deformed Volterra equation associated with linear rescaling to the general non-linear rescaling is obtained.

Tree models are broadly used in multimedia applications, but it is a challenge task to deform trees with plenty of branches. We propose a novel method to deform the tree model interactively using cages based on trees' property, and we design a framework to control the hierarchy deformation of trees. The bounding box of the trunk is used as the global control cage, while the bounding boxes of br...

We analyze the vacuum structure of N = 1/2 chiral supersymmetric theories in deformed superspace. In particular we study O’Raifeartaigh models with C-deformed superpotentials and canonical and non-canonical deformed Kähler potentials. We find conditions under which the vacuum configurations are affected by the deformations.

We consider GL q (N)-covariant quantum algebras with generators satisfying quadratic polynomial relations. We show that, up to some inessential arbitrari-ness, there are only two kinds of such quantum algebras, namely, the algebras with q-deformed commutation and q-deformed anticommutation relations. The connection with the bicovariant differential calculus on the linear quantum groups is dissc...

Motivated by deformation quantization we investigate the algebraic GNS construction of ∗representations of deformed ∗-algebras over ordered rings and compute their classical limit. The question if a GNS representation can be deformed leads to the deformation of positive linear functionals. Various physical examples from deformation quantization like the Bargmann-Fock and the Schrödinger represe...

A bicomplex is a simple mathematical structure, in particular associated with completely integrable models. The conditions defining a bicomplex are a special form of a parameter-dependent zero curvature condition. We generalize the concept of a Darboux matrix to bicomplexes and use it to derive Bäcklund transformations for several models. The method also works for Moyal-deformed equations with ...

A general Lagrangian formulation of integrably deformed G/H-coset models is given. We consider the G/H-coset model in terms of the gauged Wess-Zumino-Witten action and obtain an integrable deformation by adding a potential energy term Tr(gTgT̄ ), where algebra elements T, T̄ belong to the center of the algebra h associated with the subgroup H. We show that the classical equation of motion of the ...

An action is constructed that gives an arbitrary equation in the KdV or MKdV hierarchies as equation of motion; the second Hamiltonian structure of the KdV equation and the Hamiltonian structure of the MKdV equation appear as Poisson bracket structures derived from this action. Quantization of this theory can be carried out in two different schemes, to obtain either the quantum KdV theory of Ku...

We study the SU(2)k/U(1)-parafermion model perturbed by its first thermal operator. By formulating the theory in terms of a (perturbed) fermionic coset model we show that the model is equivalent to interacting WZW fields modulo free fields. In this scheme, the order and disorder operators of the Zk parafermion theory are constructed as gauge invariant composites. We find that the theory present...

We introduce a generalization of Ar-type Toda theory based on a non-abelian group G, which we call the (Ar, G)-Toda theory, and its affine extensions in terms of gauged Wess-Zumino-Witten actions with deformation terms. In particular, the affine (A1, SU(2))Toda theory describes the integrable deformation of the minimal conformal theory for the critical Ising model by the operator Φ(2,1). We der...