Related papers: On topological interpretation of quantum numbers
A generalization of the concept of PT-symmetric Hamiltonians H=p^2+V(x) is described. It uses analytic potentials V(x) (with singularities) and a generalized concept of PT-symmetric asymptotic boundary conditions. Nontrivial toboggans are…
In this Article we address the definition and values of topological numbers of the manifolds of wavefunctions - bands obtained by quantum superposition of the wavefunctions that belong to topologically distinct manifolds. The problem,…
Based on the notion of a $\Delta$-group(oid), ring-valued invariants of pairs of topological spaces can be defined in intrinsic topological terms.
In this paper, we collect some technical results about weights on C*-algebras which are useful in de theory of locally compact quantum groups in the C*-algebra framework. We discuss the extension of a lower semi-continuous weight to a…
We determine the homological residue fields, in the sense of tensor-triangular geometry, in a series of concrete examples ranging from topological stable homotopy theory to modular representation theory of finite groups.
Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum…
For a semisimple real Lie group $G$, we study topological properties of moduli spaces of polystable parabolic $G$-Higgs bundles over a Riemann surface with a divisor of finitely many distinct points. For a split real form of a complex…
We investigate the topological defects in phenomenological models describing mixtures of charged condensates with commensurate electric charges. Such situations are expected to appear for example in liquid metallic deuterium. This is…
Photonic modes exhibiting a polarization winding akin to a vortex possess an integer topological charge. Lasing with topological charge 1 or 2 can be realized in periodic lattices of up to six-fold rotational symmetry. Higher order charges…
We investigate 2d $\mathcal{N}=(0,4)$ supersymmetric theories obtained from a topologically-twisted reduction of 4d $\mathcal{N}=2$ class $\mathcal{S}$ theories on a Riemann surface. This study addresses subtle aspects of central charges,…
Let L be a Lie group and Lambda a lattice in L. Suppose G is a non-compact simple Lie group realized as a Lie subgroup of L, and the image of G on L/Lambda is dense. Let c be a diagonalizable element of G not contained in a compact…
The physical interpretation of the main notions of the quantum group theory (coproduct, representations and corepresentations, action and coaction) is discussed using the simplest examples of $q$-deformed objects (quantum group…
There are theories of coverings of $C^*$-algebras which can be included into a following list: coverings of commutative $C^*$-algebras, coverings of $C^*$-algebras of groupoids and foliations, coverings of noncommutative tori, the double…
We define a new class of integrable vertex models associated to quantum groups at roots of unit
The relativistic two-particle quantum mixtures are studied from the topological point of view. The mixture field variables can be transformed in such a way that a kinematical decoupling of both particle degrees of freedom takes place with a…
We consider gauge theories on noncommutative euclidean space . In particular, we discuss the structure of gauge group following standard mathematical definitions and using the ideas of hep-th/0102182.
We establish several new topological generation results for the quantum permutation groups $S^+_N$ and the quantum reflection groups $H^{s+}_N$. We use these results to show that these quantum groups admit sufficiently many "matrix models".…
We define ''convergence'' for noncommutative power series and construct two topologies on the algebra of power series, convergent with respect to a positive radius. We indicate all finite dimensional continuous representations of this…
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…
A construction of integration, function calculus, and exterior calculus is made, allowing for integration of unital magma valued functions against (compactified) unital magma valued measures over arbitrary topological spaces. The Riemann…