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Author

Harald Grosse

Other affiliations: CERN, Schrödinger
Bio: Harald Grosse is an academic researcher from University of Vienna. The author has contributed to research in topics: Noncommutative geometry & Quantum field theory. The author has an hindex of 44, co-authored 201 publications receiving 6895 citations. Previous affiliations of Harald Grosse include CERN & Schrödinger.


Papers
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TL;DR: In this article, the authors prove that the real four-dimensional Euclidean noncommutative ϕ4 model is renormalisable to all orders in perturbation theory.
Abstract: We prove that the real four-dimensional Euclidean noncommutative ϕ4-model is renormalisable to all orders in perturbation theory. Compared with the commutative case, the bare action of relevant and marginal couplings contains necessarily an additional term: an harmonic oscillator potential for the free scalar field action. This entails a modified dispersion relation for the free theory, which becomes important at large distances (UV/IR-entanglement). The renormalisation proof relies on flow equations for the expansion coefficients of the effective action with respect to scalar fields written in the matrix base of the noncommutative ℝ4. The renormalisation flow depends on the topology of ribbon graphs and on the asymptotic and local behaviour of the propagator governed by orthogonal Meixner polynomials.

536 citations

Journal ArticleDOI
TL;DR: In this paper, the authors prove that the real four-dimensional Euclidean noncommutative φ^4 model is renormalisable to all orders in perturbation theory.
Abstract: We prove that the real four-dimensional Euclidean noncommutative \phi^4-model is renormalisable to all orders in perturbation theory. Compared with the commutative case, the bare action of relevant and marginal couplings contains necessarily an additional term: an harmonic oscillator potential for the free scalar field action. This entails a modified dispersion relation for the free theory, which becomes important at large distances (UV/IR-entanglement). The renormalisation proof relies on flow equations for the expansion coefficients of the effective action with respect to scalar fields written in the matrix base of the noncommutative R^4. The renormalisation flow depends on the topology of ribbon graphs and on the asymptotic and local behaviour of the propagator governed by orthogonal Meixner polynomials.

469 citations

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TL;DR: In this article, a self-interacting scalar field on a truncated sphere is described and quantized using the functional (path) integral approach, which possesses full symmetry with respect to the isometries of the sphere.
Abstract: We describe a self-interacting scalar field on a truncated sphere and perform the quantization using the functional (path) integral approach. The theory possesses full symmetry with respect to the isometries of the sphere. We explicitly show that the model is finite and that UV regularization automatically takes place.

263 citations

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TL;DR: The renormalisation of Euclidean two-dimensional noncommutative \phi^4-theory has been shown to be renormalizable in momentum space.
Abstract: As a first application of our renormalisation group approach to non-local matrix models [hep-th/0305066], we prove (super-)renormalisability of Euclidean two-dimensional noncommutative \phi^4-theory. It is widely believed that this model is renormalisable in momentum space arguing that there would be logarithmic UV/IR-divergences only. Although momentum space Feynman graphs can indeed be computed to any loop order, the logarithmic UV/IR-divergence appears in the renormalised two-point function -- a hint that the renormalisation is not completed. In particular, it is impossible to define the squared mass as the value of the two-point function at vanishing momentum. In contrast, in our matrix approach the renormalised N-point functions are bounded everywhere and nevertheless rely on adjusting the mass only. We achieve this by introducing into the cut-off model a translation-invariance breaking regulator which is scaled to zero with the removal of the cut-off. The naive treatment without regulator would not lead to a renormalised theory.

225 citations

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TL;DR: In this article, the authors describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory on the lattice which is expected to reproduce the results of the continuous theory exactly.
Abstract: Motivated by a recent paper of Fock and Rosly [6] we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which is expected to reproduce the results of the continuous theory exactly. The lattice model enjoys the symmetry with respect to a quantum gauge group. Using this fact we construct the algebra of observables of the Hamiltonian Chern-Simons theory equipped with a *- operation and a positive inner product.

209 citations


Cited by
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TL;DR: The generalization of field theory to space-time with noncommuting coordinates has been studied intensively in the last few years and many qualitatively new phenomena have been discovered, on both the classical and quantum level as discussed by the authors.
Abstract: This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level.

2,306 citations

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TL;DR: In this article, a pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity.

1,752 citations

01 Jan 2016
TL;DR: The methods of modern mathematical physics is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly.
Abstract: Thank you very much for reading methods of modern mathematical physics. Maybe you have knowledge that, people have look numerous times for their favorite novels like this methods of modern mathematical physics, but end up in harmful downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some infectious virus inside their desktop computer. methods of modern mathematical physics is available in our digital library an online access to it is set as public so you can download it instantly. Our books collection saves in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the methods of modern mathematical physics is universally compatible with any devices to read.

1,536 citations

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TL;DR: In this article, uncertainty relations for the different coordinates of spacetime events are proposed, motivated by Heisenberg's principle and by Einstein's theory of classical gravity, and a model of Quantum Spacetime is discussed where the commutation relations exactly implement our uncertainty relations.
Abstract: We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg's principle and by Einstein's theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation relations exactly implement our uncertainty relations.

1,453 citations

Journal Article
TL;DR: In this article, the fundamental isomorphism theorem of π-algebras is proved and some algebraic properties of Hopf π algebbras are studied.
Abstract: This paper introduces five notions, including π-algebras, π-ideals, Hopf π-algebras, π-modules and Hopf π-modules, verifies the fundamental isomorphism theorem of π-algebras and studies some algebraic properties of Hopf π-algebras as well.

1,322 citations