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Related papers: The quantum metric structure of quantum SU(2)

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We extend the Gromov-Hausdorff propinquity to a metric on Lipschitz dynamical systems, which are given by strongly continuous actions of proper monoids on quantum compact metric spaces via Lipschitz morphisms. We prove that our resulting…

Operator Algebras · Mathematics 2020-10-15 Frederic Latremoliere

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…

Mathematical Physics · Physics 2018-02-22 Timothé Poulain , Jean-Christophe Wallet

Quantifying quantum resources for simulating the fundamental forces of Nature is sensitive to the mapping of gauge fields onto finite quantum computational architectures. When locally truncating lattice gauge theories in the irreducible…

Quantum Physics · Physics 2026-05-15 Zoë Webb-Mack , Natalie Klco

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.…

High Energy Physics - Theory · Physics 2014-11-18 E. Cremmer , J. -L. Gervais , J. Schnittger

We present a tomographic scheme, based on spacetime symmetries, for the reconstruction of the internal degrees of freedom of a Dirac spinor. We discuss the circumstances under which the tomographic group can be taken as SU(2), and how this…

Quantum Physics · Physics 2007-05-23 Ricardo A. Mosna , Jayme Vaz

The Podles quantum sphere S^2_q admits a natural commutative C*-subalgebra I_q with spectrum {0} \cup {q^{2k}: k = 0,1,2,...}, which may therefore be considered as a quantised version of a classical interval. We study here the compact…

Operator Algebras · Mathematics 2021-03-12 Thomas Gotfredsen , Jens Kaad , David Kyed

Three-dimensional bicovariant differential calculus on the quantum group SU_q(2) is constructed using the approach based on global covariance under the action of the stabilizing subgroup U(1). Explicit representations of possible q-deformed…

High Energy Physics - Theory · Physics 2007-05-23 D. G. Pak

Gravitational subsystems with boundaries carry the action of an infinite-dimensional symmetry algebra, with potentially profound implications for the quantum theory of gravity. We initiate an investigation into the quantization of this…

High Energy Physics - Theory · Physics 2023-06-21 William Donnelly , Laurent Freidel , Seyed Faroogh Moosavian , Antony J. Speranza

Exact procedures that follow Dirac's constraint quantization of gauge theories are usually technically involved and often difficult to implement in practice. We overview an "effective" scheme for obtaining the leading order semiclassical…

Mathematical Physics · Physics 2015-05-14 Artur Tsobanjan

We introduce $*$-structures on braided groups and braided matrices. Using this, we show that the quantum double $D(U_q(su_2))$ can be viewed as the quantum algebra of observables of a quantum particle moving on a hyperboloid in q-Minkowski…

High Energy Physics - Theory · Physics 2008-02-03 Shahn Majid

Following a suggestion by Vafa, we present a quantum-mechanical model for S-duality symmetries observed in the quantum theories of fields, strings and branes. Our formalism may be understood as the topological limit of Berezin's metric…

High Energy Physics - Theory · Physics 2009-10-31 J. M. Isidro

In the framework of Dirac quantization, the SU(2) Skyrmion is canonically quantized to yield the modified predictions of the static properties of baryons. We show that the energy spectrum of this Skyrmion obtained by the Dirac method with…

High Energy Physics - Theory · Physics 2009-10-31 Soon-Tae Hong , Yong-Wan Kim , Young-Jai Park

The Dolbeault complex of a quantized compact Hermitian symmetric space is expressed in terms of the Koszul complex of a braided symmetric algebra of Berenstein and Zwicknagl. This defines a spectral triple quantizing the Dolbeault-Dirac…

Quantum Algebra · Mathematics 2014-12-23 Ulrich Kraehmer , Matthew Tucker-Simmons

We solve for spectrum, obtain explicitly and study group properties of eigenfunctions of Dirac operator on the Riemann sphere $S^2$. The eigenvalues $\lambda$ are nonzero integers. The eigenfunctions are two-component spinors that belong to…

High Energy Physics - Theory · Physics 2007-05-23 A. A. Abrikosov

The q-deformed fuzzy Dirac and chirality operators on quantum fuzzy four-sphere $ S^{4}_{qF} $. Using the q-deformed fuzzy Ginsparg-Wilson algebra, it has been studied the q-deformed fuzzy Dirac and chirality operators in instanton and…

High Energy Physics - Theory · Physics 2021-02-24 Mehdi Lotfizadeh

We study a notion of non-commutative integration, in the spirit of modular spectral triples, for the quantum group $SU_{q}(2)$. In particular we define the non-commutative integral as the residue at the spectral dimension of a zeta…

Mathematical Physics · Physics 2015-06-22 Marco Matassa

We study completely positive and trace-preserving equivariant maps between operators on irreducible representations of $\mathrm{SU}(2)$. We find asymptotic approximations of channels in the limit of large output representation and we…

Mathematical Physics · Physics 2025-08-28 Tommaso Aschieri , Błażej Ruba , Jan Philip Solovej

In this paper, following [1], we develop the theory of global pseudo-differential operators defined on the quantum group $SU_q(2)$, and provide some spectral results concerning these operators. We define a graduation for this algebra of…

Quantum Algebra · Mathematics 2018-04-03 Carlos Andres Rodriguez Torijano

There are only two quantum group structures on the space of two by two unimodular matrices, these are the $SL_q(2)$ and the $SL_h(2)$ [9-13] quantum groups. One can not construct a differential geometry on $ SL_q(2)$, which at the same time…

High Energy Physics - Theory · Physics 2009-10-28 Vahid Karimipour

We use the theory of Berezin-Toeplitz operators of Ma and Marinescu to study the quantum Hamiltonian dynamics associated with classical Hamiltonian flows over closed prequantized symplectic manifolds in the context of geometric quantization…

Differential Geometry · Mathematics 2020-03-03 Louis Ioos