Related papers: Some Noncommutative Geometric Aspects of SU_q(2)
Using the Dirac (Clifford) algebra $\gamma^{\mu}$ as initial stage of our discussion, we summarize and extend previous work with respect to the isomorphic 15dimensional Lie algebra su$*$(4) as complex embedding of sl(2,$\mathbb{H}$), the…
We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on $SU_q(2)$ . The…
It is well-known that the tight-binding Hamiltonian of graphene describes the low-energy excitations that appear to be massless chiral Dirac fermions. Thus, in the continuum limit one can analyze the crystal properties using the formalism…
Coherent states on the quantum group $SU_q(2)$ are defined by using harmonic analysis and representation theory of the algebra of functions on the quantum group. Semiclassical limit $q\rightarrow 1$ is discussed and the crucial role of…
We present a recent work on the Dirac equation in a curved spacetime. In addition to the standard equation, two alternative versions are considered, derived from wave mechanics, and based on the tensor representation of the Dirac field. The…
We show that the N=2 superextended 1D quantum Dirac delta potential problem is characterized by the hidden nonlinear $su(2|2)$ superunitary symmetry. The unexpected feature of this simple supersymmetric system is that it admits three…
We discuss necessary conditions for a compact quantum group to act on the algebra of noncommutative $n$-torus $\mathbb{T}_\theta^n$ in a filtration preserving way in the sense of Banica and Skalski. As a result, we construct a family of…
By combining the generalized exterior algebra of forms over a noncommutative algebra with the gauging of discrete directions and the associated Higgs fields, we consider the construction of the bosonic sector of left-right symmetric models…
Starting with a Hilbert space endowed with a representation of a unitary Lie algebra and an action of a generalized Dirac operator, we develop a mathematical concept towards gauge field theories. This concept shares common features with the…
This is the first installment of a paper in three parts, where we use noncommutative geometry to study the space of commensurability classes of Q-lattices and we show that the arithmetic properties of KMS states in the corresponding quantum…
We study the algebraic structure of the one-dimensional Dirac oscillator by extending the concept of spin symmetry to a noncommutative case. An SO(4) algebra is found connecting the eigenstates of the Dirac oscillator, in which the two…
We initiate the study of a q-deformed geometry for quantum SU(2). In contrast with the usual properties of a spectral triple, we get that only twisted commutators between algebra elements and our Dirac operator are bounded. Furthermore, the…
In our previous publications we introduced differential calculus on the enveloping algebras U(gl(m)) similar to the usual calculus on the commutative algebra Sym(gl(m)). The main ingredient of our calculus are quantum partial derivatives…
A matricial Darboux operator intertwining two one-dimensional stationary Dirac Hamiltonians is constructed. This operator is such that the potential of the second Dirac Hamiltonian as well as the corresponding eigenfunctions are determined…
Quantum spaces with $\frak{su}(2)$ noncommutativity can be modelled by using a family of $SO(3)$-equivariant differential $^*$-representations. The quantization maps are determined from the combination of the Wigner theorem for $SU(2)$ with…
We study some classes of symmetric operators for the discrete series representations of the quantum algebra U_q(su_{1,1}), which may serve as Hamiltonians of various physical systems. The problem of diagonalization of these operators…
A general two qubit system expressed in terms of the complete set of unit and fifteen traceless, Hermitian Dirac matrices, is shown to exhibit novel features of this system. The well-known physical interpretations associated with the…
Wilson observables for 2+1 quantum gravity with negative cosmological constant, when the spatial manifold is a torus, exhibit several novel features: signed area phases relate the observables assigned to homotopic loops, and their…
We study the nonclassical properties and algebraic characteristics of the negative binomial states introduced by Barnett recently. The ladder operator formalism and displacement operator formalism of the negative binomial states are found…
In a previous paper, we proposed a construction of $U_q(sl(2))$ quantum group symmetry generators for 2d gravity, where we took the chiral vertex operators of the theory to be the quantum group covariant ones established in earlier works.…