相关论文: On q-Deformed Supersymmetric Classical Mechanical …

We consider a 3-parametric linear deformation of the Poisson brackets in classical mechanics. This deformation can be thought of as the classical limit of dynamics in so-called "quantized spaces". Our main result is a description of the…

The ($p=2$) parabose-parafermi supersymmetry is studied in general terms. It is shown that the algebraic structure of the ($p=2$) parastatistical dynamical variables allows for (symmetry) transformations which mix the parabose and parafermi…

We investigate supergroups with Grassmann parameters replaced by odd Clifford parameters. The connection with non-anticommutative supersymmetry is discussed. A Berezin-like calculus for odd Clifford variables is introduced. Fermionic…

Attention is focused on antisymmetrized versions of quantum spaces that are of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski…

The Gauss decompositions of the quantum groups, related to classical Lie groups and supergroups are considered by the elementary algebraic and $R$-matrix methods. The commutation relations between new basis generators (which are introduced…

Phase-space realisations of an infinite parameter family of quantum deformations of the boson algebra in which the $q$-- and the $qp$--deformed algebras arise as special cases are studied. Quantum and classical models for the corresponding…

We consider canonically conjugated generalized space and linear momentum operators $\hat{x}_q$ and $ \hat{p}_q$ in quantum mechanics, associated to a generalized translation operator which produces infinitesimal deformed displacements…

The scalar fields of supersymmetric models are coordinates of a geometric space. We propose a formulation of supersymmetry that is covariant with respect to reparametrizations of this target space. Employing chiral multiplets as an example,…

We deform the standard four dimensional $\N=1$ superspace by making the odd coordinates $\theta$ not anticommuting, but satisfying a Clifford algebra. Consistency determines the other commutation relations of the coordinates. In particular,…

We present the N=2 supersymmetric formulation for the classical and quantum dynamics of a nonrelativistic charged particle on a curved surface in the presence of a perpendicular magnetic field. For a particle moving on a constant-curvature…

We consider a quantum group interpretation of the non-anticommutative deformations in Euclidean supersymmetric theories. Twist deformations in the corresponding superspaces and Lie superalgebras are constructed in terms of the left…

The class of relativistic spin particle models reveals the `quantization' of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same…

We define a manifestly supersymmetric version of the $T \overline{T}$ deformation appropriate for a class of $(0+1)$-dimensional theories with $\mathcal{N} = 1$ or $\mathcal{N} = 2$ supersymmetry, including one presentation of the…

Two supersymmetric classical mechanical systems are discussed. Concrete realizations are obtained by supposing that the dynamical variables take values in a Grassmann algebra with two generators. The equations of motion are explicitly…

In quantum field theory the creation and annihilation operators that are located at the points in 3-momentum space have commutation relations that are conserved under the action of a $U({\infty})$ group. Here it is shown how to define an…

We present the quantum and classical mechanics formalisms for a particle with position-dependent mass in the context of a deformed algebraic structure (named $\kappa$-algebra), motivated by the Kappa-statistics. From this structure we…

We numerically study Barrett-Crane models of Riemannian quantum gravity. We have extended the existing numerical techniques to handle q-deformed models and arbitrary space-time triangulations. We present and interpret expectation values of…

The q-deformed traces and orbits for the two parametric quantum groups $GL_{qp}(2)$ and $GL_{qp}(1|1)$ are defined. They are subsequently used in the construction of $q$-orbit invariants for these groups. General $qp$-(super)oscillator…

We define a generalized $(q;\alpha,\beta,\gamma;\nu)$-deformed oscillator algebra and study the number of its characteristics. We describe the structure function of deformation, analyze the classification of irreducible representations and…

We propose a manifestly supersymmetric generalization of the solvable $T \overline{T}$ deformation of two-dimensional field theories. For theories with $(1,1)$ and $(0,1)$ supersymmetry, the deformation is defined by adding a term to the…