Author
Andrzej Sitarz
Other affiliations: University of Paris, Polish Academy of Sciences, University of Mainz ...read more
Bio: Andrzej Sitarz is an academic researcher from Jagiellonian University. The author has contributed to research in topics: Noncommutative geometry & Dirac operator. The author has an hindex of 28, co-authored 146 publications receiving 2603 citations. Previous affiliations of Andrzej Sitarz include University of Paris & Polish Academy of Sciences.
Papers published on a yearly basis
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TL;DR: In this article, it was shown that there is no 4D bicovariant differential calculus which are Lorentz covariant, however, there exists a five-dimensional differential calculus, which satisfies both requirements.
Abstract: Following the construction of the $\kappa$-Minkowski space from the bicrossproduct structure of the $\kappa$-Poincare group, we investigate possible differential calculi on this noncommutative space. We discuss then the action of the Lorentz quantum algebra and prove that there are no 4D bicovariant differential calculi, which are Lorentz covariant. We show, however, that there exist a five-dimensional differential calculus, which satisfies both requirements. We study also a toy example of 2D $\kappa$-Minkowski space and and we briefly discuss the main properties of its differential calculi.
139 citations
TL;DR: In this article, a 3+summable spectral triple Open Image in new window over the quantum group SUq(2) which is equivariant with respect to a left and a right action was constructed.
Abstract: We construct a 3+-summable spectral triple Open image in new window over the quantum group SUq(2) which is equivariant with respect to a left and a right action of Open image in new window The geometry is isospectral to the classical case since the spectrum of the operator D is the same as that of the usual Dirac operator on the 3-dimensional round sphere. The presence of an equivariant real structure J demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order.
134 citations
TL;DR: In this paper, it was shown that there are no 4D bicovariant differential calculi, which are Lorentz covariant, and that there exists a five-dimensional differential calculus, which satisfies both requirements.
130 citations
TL;DR: In this article, the authors classify zero-dimensional spectral triples over complex and real algebras and provide some general statements about their differential structure, including whether such triples admit a symmetry arising from the Hopf algebra structure of the finite algebra.
Abstract: We classify zero-dimensional spectral triples over complex and real algebras and provide some general statements about their differential structure. We investigate also whether such spectral triples admit a symmetry arising from the Hopf algebra structure of the finite algebra. We discuss examples of commutative algebras and group algebras.
114 citations
TL;DR: In this article, the authors derived the algebraic part of the real spectral triple data for the standard Podle's quantum sphere: equivariant representation, chiral grading, reality structure, and Dirac operator.
Abstract: Using principles of quantum symmetries we derive the algebraic part of the real spectral triple data for the standard Podle\'s quantum sphere: equivariant representation, chiral grading $\gamma$, reality structure $J$ and the Dirac operator $D$, which has bounded commutators with the elements of the algebra and satisfies the first order condition.
97 citations
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TL;DR: Chari and Pressley as mentioned in this paper have published a book called "Chari, Pressley, and Chari: A Conversation with Vyjayanthi Chari and Andrew Pressley".
Abstract: By Vyjayanthi Chari and Andrew Pressley: 651 pp., £22.95 (US$34.95), isbn 0 521 55884 0 (Cambridge University Press, 1994).
761 citations
TL;DR: This work reviews the current status of phenomenological programs inspired by quantum-spacetime research and stresses the significance of results establishing that certain data analyses provide sensitivity to effects introduced genuinely at the Planck scale.
Abstract: I review the current status of phenomenological programs inspired by quantum-spacetime research. I stress in particular the significance of results establishing that certain data analyses provide sensitivity to effects introduced genuinely at the Planck scale. My main focus is on phenomenological programs that affect the directions taken by studies of quantum-spacetime theories.
642 citations
Book•
01 Jan 2007TL;DR: In this article, the Riemann zeta function and non-commutative spaces are studied in the context of quantum statistical mechanics and Galois symmetries, including the Weil explicit formula.
Abstract: Quantum fields, noncommutative spaces, and motives The Riemann zeta function and noncommutative geometry Quantum statistical mechanics and Galois symmetries Endomotives, thermodynamics, and the Weil explicit formula Appendix Bibliography Index.
573 citations
Book•
23 Aug 2014
TL;DR: The Spectral Calculus as mentioned in this paper is a generalization of K-theory for non-commutative spaces and algebraic spaces and algebras of functions, and it is used in Projective Systems of Non-Commutative Lattices.
Abstract: Noncommutative Spaces and Algebras of Functions.- Projective Systems of Noncommutative Lattices.- Modules as Bundles.- A Few Elements of K-Theory.- The Spectral Calculus.- Noncommutative Differential Forms.- Connections on Modules.- Field Theories on Modules.- Gravity Models.- Quantum Mechanical Models on Noncommutative Lattices.
572 citations
TL;DR: In this article, a deformation of infinitesimal diffeomorphisms of a smooth manifold is studied and a differential geometry on a noncommutative algebra of functions whose product is a star product is developed.
Abstract: We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star product. The class of noncommutative spaces studied is very rich. Non-anticommutative superspaces are also briefly considered. The differential geometry developed is covariant under deformed diffeomorphisms and is coordinate independent. The main target of this work is the construction of Einstein's equations for gravity on noncommutative manifolds.
467 citations