Related papers: Twisted h-spacetimes and invariant equations
The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…
By invoking the concept of twisted Poincar\' e symmetry of the algebra of functions on a Minkowski space-time, we demonstrate that the noncommutative space-time with the commutation relations $[x_\mu,x_\nu]=i\theta_{\mu\nu}$, where…
We study deformations of orbit closures for the action of a connected semisimple group $G$ on its Lie algebra $\mathfrak{g}$, especially when $G$ is the special linear group. The tools we use are on the one hand the invariant Hilbert scheme…
The light-cone gauge approach to $T\overline{T}$ deformed models is used to derive the $T\overline{T}$ deformed matrix nonlinear Schr\"odinger equation, the Landau--Lifshitz equation, and the Gardner equation. Properties of one-soliton…
This work addresses the Hamiltonian dynamics of the Kepler problem in a deformed phase space, by considering the equatorial orbit. The recursion operators are constructed and used to compute the integrals of motion. The same investigation…
We give a formulation of a deformation of Dirac operator along orbits of a group action on a possibly non-compact manifold to get an equivariant index and a K-homology cycle representing the index. We apply this framework to non-compact…
h-deformation of (graded) Hopf algebra of functions on supergroup GL(1|1) is introduced via a contration of GL_q (1|1). The deformation parameter h is odd (grassmann). Related differential calculus on h-superplane is presented.
We study a class of Hamiltonian deformations of the massless Einstein-Klein-Gordon system in spherical symmetry for which the Dirac constraint algebra closes. The system may be regarded as providing effective equations for quantum…
We treat spectral problems by twisted groupoid methods. To Hausdorff locally compact groupoids endowed with a continuous $2$-cocycle one associates the reduced twisted groupoid $C^*$-algebra. Elements (or multipliers) of this algebra admit…
In this paper, we study the algebra of twisted vertex operators over an even integral ${\mathbf Z}_2$-lattice, and give a kind of systematic construction of fundamental representations for affine Lie algebras of type $A$, $D$, $E$ with…
We establish global existence and derive sharp pointwise decay estimates of solutions to cubic Dirac and Dirac-Klein-Gordon systems on a curved background, close to the Minkowski spacetime. By squaring the Dirac operator, we reduce the…
In this paper we study the deformed statistics and oscillator algebras of quantum fields defined in $\kappa$-Minkowski spacetime. The twisted flip operator obtained from the twist associated with the star product requires an enlargement of…
We study the deformations of twisted harmonic maps $f$ with respect to the representation $\rho$. After constructing a continuous "universal" twisted harmonic map, we give a construction of every first order deformation of $f$ in terms of…
We describe the twisted space-time symmetries which imply the quantum Poincar\'{e} covariance of noncommutative Minkowski spaces, with constant, Lie algebraic and quadratic commutators. Further we present the relativistic and…
We investigated the effects of the global monopole spacetime on the Dirac and Klein-Gordon relativistic quantum oscillators. In order to do this, we solve the Dirac and Klein-Gordon equations analytically and discuss the influence of this…
In the present work, we studied the q-deformed Morse and harmonic oscillator systems with appropriate canonical commutation algebra. The analytic solutions for eigenfunctions and energy eigenvalues are worked out using time-independent…
The three new deformed Poincare Hopf algebras are constructed with use of twist procedure. The corresponding relativistic space-times providing the sum of canonical and Lie-algebraic type of noncommutativity are proposed. Finally, the…
We consider two different types of deformations for the linear group $ GL(n)$ which correspond to using of a general diagonal R-matrix. Relations between braided and quantum deformed algebras and their coactions on a quantum plane are…
We prove under certain assumptions that there exists a solution of the Schrodinger or the Heisenberg equation of motion generated by a linear operator H acting in some complex Hilbert space H, which may be unbounded, not symmetric, or not…
The description of the $T\bar{T}$ deformation in terms of two-dimensional gravity is analyzed from the Hamiltonian point of view, in a manner analogous to the ADM description of general relativity. We find that the Hamiltonian constraints…