Monopoles, Dirac operator, and index theory for fuzzy<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo stretchy="false">/</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>×</mml:mo><mml:mi>U</mml:mi><mml:mo stretchy=

Acharyya, Nirmalendu; Díez, Verónica V. Errasti

doi:10.1103/physrevd.90.125034

Cited by 3 publications

(2 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In several earlier papers [31, 33,35,36] I showed how to give a precise meaning to statements in the literature of high-energy physics and string theory of the kind "matrix algebras converge to the sphere". (See the references to the quantum physics literature given in [31,34,41,9,11,3,1].) I did this by introducing and developing a concept of "compact quantum metric spaces", and a corresponding quantum Gromov-Hausdorff-type distance between them.…”

Section: Introductionmentioning

confidence: 99%

Vector bundles for “Matrix algebras converge to the sphere”

Rieffel

2018

Journal of Geometry and Physics

View full text Add to dashboard Cite

In the high-energy quantum-physics literature, one finds statements such as "matrix algebras converge to the sphere". Earlier I provided a general precise setting for understanding such statements, in which the matrix algebras are viewed as quantum metric spaces, and convergence is with respect to a quantum Gromov-Hausdorff-type distance.But physicists want even more to treat structures on spheres (and other spaces), such as vector bundles, Yang-Mills functionals, Dirac operators, etc., and they want to approximate these by corresponding structures on matrix algebras. In the present paper we treat this idea for vector bundles. We develop a general precise way for understanding how, for two compact quantum metric spaces that are close together, to a given vector bundle on one of them there can correspond in a natural way a unique vector bundle on the other. We then show explicitly how this works for the case of matrix algebras converging to the 2-sphere.

show abstract

Section: Introductionmentioning

confidence: 99%

Vector bundles for “Matrix algebras converge to the sphere”

Rieffel

2018

Journal of Geometry and Physics

View full text Add to dashboard Cite

show abstract

“…In several earlier papers [11,12,14] I showed how to give a precise meaning to statements in the literature of high-energy physics and string theory of the kind "matrix algebras converge to the sphere". (See the references to the quantum physics literature given in [11,13,15,4,5,2,1].) I did this by introducing and developing a concept of "compact quantum metric spaces", and a corresponding quantum Gromov-Hausdorff-type distance between them.…”

Section: Introductionmentioning

confidence: 99%

Matricial bridges for “Matrix algebras converge to the sphere”

Rieffel¹

2016

Operator Algebras and Their Applications

View full text Add to dashboard Cite

In the high-energy quantum-physics literature one finds statements such as "matrix algebras converge to the sphere". Earlier I provided a general setting for understanding such statements, in which the matrix algebras are viewed as quantum metric spaces, and convergence is with respect to a quantum Gromov-Hausdorfftype distance. In the present paper, as preparation of discussing similar statements for convergence of "vector bundles" over matrix algebras to vector bundles over spaces, we introduce and study suitable matrix-norms for matrix algebras and spaces. Very recently Latrémoliere introduced an improved quantum Gromov-Hausdorfftype distance between quantum metric spaces. We use it throughout this paper. To facilitate the calculations we introduce and develop a general notion of "bridges with conditional expectations".2010 Mathematics Subject Classification. Primary 46L87; Secondary 53C23, 58B34, 81R15, 81R30 .

show abstract

Fuzzy conifold YF6 and Dirac operator of principal fibration XF5 → SF2 × SF2

Lotfizadeh

2020

Int. J. Mod. Phys. A

View full text Add to dashboard Cite

It has been constructed the fuzzy Dirac and chirality operators on fuzzy [Formula: see text] which is the base manifold of the principal fibration [Formula: see text]. Using the fuzzy Ginsparg–Wilson algebra, it has been studied the gauged fuzzy Dirac and chirality operators in instanton sector. It has been shown that they have correct commutative limit in the limit case when noncommutative parameter [Formula: see text] tends to infinity.

show abstract

Monopoles, Dirac operator, and index theory for fuzzySU(3)/(U(1)×U

Cited by 3 publications

References 24 publications

Vector bundles for “Matrix algebras converge to the sphere”

Vector bundles for “Matrix algebras converge to the sphere”

Matricial bridges for “Matrix algebras converge to the sphere”

Fuzzy conifold YF6 and Dirac operator of principal fibration XF5 → SF2 × SF2

Contact Info

Product

Resources

About