Related papers: Quantum deformed magnon kinematics
Starting from generalized position operators, we derive complex and quaternionic angular momentum operators along with their commutation algebra as well. These algebras differ from the standard Hermitian ones, especially in terms of…
In this article we present formulae for q-integration on quantum spaces which could be of particular importance in physics, i.e. q-deformed Minkowski space and q-deformed Euclidean space in 3 or 4 dimensions. Furthermore, our formulae can…
The corner symmetry algebra organises the physical charges induced by gravity on codimension-$2$ corners of a manifold. In this letter, we initiate a study of the quantum properties of this group using as a toy model the corner symmetry…
We review the W_N algebra and its quantum deformation, based on free field realizations. The (quantum deformed) W_N algebra is defined through the (quantum deformed) Miura transformation, and its singular vectors realize the Jack…
Deforming the algebraic structure of geometric algebra on the phase space with a Moyal product leads naturally to supersymmetric quantum mechanics in the star product formalism.
It is shown that q-deformed quantum mechanics (q-deformed Heisenberg algebra) can be interpreted as quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first-) class constraints. (Saclay, T93/027).
This work addresses the study of the oscillator algebra, defined by four parameters $p$, $q$, $\alpha$, and $\nu$. The time-independent Schr\"{o}dinger equation for the induced deformed harmonic oscillator is solved; explicit analytic…
With a q-deformed quantum mechanical framework, features of the uncertainty relation and a novel formulation of the Schr\"odinger equation are considered.
The quantum deformed (1+1) Poincare' algebra is shown to be the kinematical symmetry of the harmonic chain, whose spacing is given by the deformation parameter. Phonons with their symmetries as well as multiphonon processes are derived from…
We investigate quantum deformation of conformal algebras by constructing the quantum space for $sl_q(4,C)$. The differential calculus on the quantum space and the action of the quantum generators are studied. We derive deformed $su(4)$ and…
We generalize the formulation of non-commutative quantum mechanics to three dimensional non-commutative space. Particular attention is paid to the identification of the quantum Hilbert space in which the physical states of the system are to…
Let $U_q(\hat{\cal G})$ be an infinite-dimensional quantum affine Lie algebra. A family of central elements or Casimir invariants are constructed and their eigenvalues computed in any integrable irreducible highest weight representation.…
A nonlinear transformation in the momentum space is constructed which converts the deformed action of Lorentz and Weyl generators on momenta into the standard one.
In this paper all deformations of the general linear group, subject to certain restrictions which in particular ensure a smooth passage to the Lie group limit, are obtained. Representations are given in terms of certains sets of creation…
We propose a mathematically rigorous unified framework for hybrid quantum mechanics that systematically combines algebraic deformation and spatial non-locality within a single operator formalism. By constructing a self-adjoint hybrid…
Quantum integrable spin chains are known to possess a large family of long-range deformations generated by the local, boost and bilocal operators. Although these deformations are well-understood on the level of the pairwise commuting…
We characterise the quantum group gauge symmetries underlying q-deformations of two-dimensional Yang-Mills theory by studying their relationships with the matrix models that appear in Chern-Simons theory and six-dimensional N=2 gauge…
A multi-shell generalization of a fermion representation of the q-deformed compact symplectic sp_q(4) algebra is introduced. An analytic form for the action of two or more generators of the Sp_q(4) symmetry on the basis states is determined…
The Hilbert space representations of a non-commutative q-deformed Minkowski space, its momenta and its Lorentz boosts are constructed. The spectrum of the diagonalizable space elements shows a lattice-like structure with accumulation points…
Curved momentum spaces associated to the $\kappa$-deformation of the (3+1) de Sitter and Anti-de Sitter algebras are constructed as orbits of suitable actions of the dual Poisson-Lie group associated to the $\kappa$-deformation with…