40 research outputs found

    Symmetries of noncommutative scalar field theory

    Full text link
    We investigate symmetries of the scalar field theory with harmonic term on the Moyal space with euclidean scalar product and general symplectic form. The classical action is invariant under the orthogonal group if this group acts also on the symplectic structure. We find that the invariance under the orthogonal group can be restored also at the quantum level by restricting the symplectic structures to a particular orbit.Comment: 12 pages, revised versio

    Induced Gauge Theory on a Noncommutative Space

    Full text link
    We discuss the calculation of the 1-loop effective action on four dimensional, canonically deformed Euclidean space. The theory under consideration is a scalar ϕ4\phi^4 model with an additional oscillator potential. This model is known to be re normalisable. Furthermore, we couple an exterior gauge field to the scalar field and extract the dynamics for the gauge field from the divergent terms of the 1-loop effective action using a matrix basis. This results in proposing an action for noncommutative gauge theory, which is a candidate for a renormalisable model.Comment: 8 page

    Renormalization of the commutative scalar theory with harmonic term to all orders

    Full text link
    The noncommutative scalar theory with harmonic term (on the Moyal space) has a vanishing beta function. In this paper, we prove the renormalizability of the commutative scalar field theory with harmonic term to all orders by using multiscale analysis in the momentum space. Then, we consider and compute its one-loop beta function, as well as the one on the degenerate Moyal space. We can finally compare both to the vanishing beta function of the theory with harmonic term on the Moyal space.Comment: 16 page

    Overview of the parametric representation of renormalizable non-commutative field theory

    Full text link
    We review here the parametric representation of Feynman amplitudes of renormalizable non-commutative quantum field models.Comment: 10 pages, 3 figures, to be published in "Journal of Physics: Conference Series

    Noncommutative geometry, gauge theory and renormalization

    Full text link
    Die nichtkommutative Geometrie bildet als wachsendes Gebiet der Mathematik einen vielversprechenden Rahmen für die moderne Physik. Quantenfeldtheorien über nichtkommutativen Räumen werden zur Zeit intensiv studiert. Sie führen zu einer neuen Art von Divergenzen, die ultraviolett-infrarot Mischung. Eine Lösung dieses Problems wurde von H. Grosse und R. Wulkenhaar durch Hinzufügen eines harmonischen Terms zur Wirkung des phi4-Modells gefunden. Dadurch wird diese Quantenfeldtheorie über dem Moyal-Raum renormierbar. Ein Ziel dieser Doktorarbeit ist die Verallgemeinerung dieses harmonischen Terms auf Eichtheorien über dem Moyal-Raum. Basierend auf dem Grosse-Wulkenhaar-Modell wird eine neue nichtkommutative Eichtheorie eingeführt, die begründete Chancen hat, renormierbar zu sein. Die wichtigsten Eigenschaften dieser Eichtheorie, insbesondere die Vakuumskonfigurationen, werden studiert. Schliesslich wird mittels eines zu einer Superalgebra assoziierten Derivationskalküls eine mathematische Interpretation dieser neuen Wirkung gegeben

    One-loop β\beta functions of a translation-invariant renormalizable noncommutative scalar model

    Full text link
    Recently, a new type of renormalizable ϕ44\phi^{\star 4}_{4} scalar model on the Moyal space was proved to be perturbatively renormalizable. It is translation-invariant and introduces in the action a a/(θ2p2)a/(\theta^2p^2) term. We calculate here the β\beta and γ\gamma functions at one-loop level for this model. The coupling constant βλ\beta_\lambda function is proved to have the same behaviour as the one of the ϕ4\phi^4 model on the commutative R4\mathbb{R}^4. The βa\beta_a function of the new parameter aa is also calculated. Some interpretation of these results are done.Comment: 13 pages, 3 figure

    Noncommutative Induced Gauge Theories on Moyal Spaces

    Full text link
    Noncommutative field theories on Moyal spaces can be conveniently handled within a framework of noncommutative geometry. Several renormalisable matter field theories that are now identified are briefly reviewed. The construction of renormalisable gauge theories on these noncommutative Moyal spaces, which remains so far a challenging problem, is then closely examined. The computation in 4-D of the one-loop effective gauge theory generated from the integration over a scalar field appearing in a renormalisable theory minimally coupled to an external gauge potential is presented. The gauge invariant effective action is found to involve, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic term, which for the noncommutative ϕ4\phi^4-theory on Moyal space ensures renormalisability. A class of possible candidates for renormalisable gauge theory actions defined on Moyal space is presented and discussed.Comment: 24 pages, 6 figures. Talk given at the "International Conference on Noncommutative Geometry and Physics", April 2007, Orsay (France). References updated. To appear in J. Phys. Conf. Se

    On the Effective Action of Noncommutative Yang-Mills Theory

    Full text link
    We compute here the Yang-Mills effective action on Moyal space by integrating over the scalar fields in a noncommutative scalar field theory with harmonic term, minimally coupled to an external gauge potential. We also explain the special regularisation scheme chosen here and give some links to the Schwinger parametric representation. Finally, we discuss the results obtained: a noncommutative possibly renormalisable Yang-Mills theory.Comment: 19 pages, 6 figures. At the occasion of the "International Conference on Noncommutative Geometry and Physics", April 2007, Orsay (France). To appear in J. Phys. Conf. Se

    Connes distance by examples: Homothetic spectral metric spaces

    Full text link
    We study metric properties stemming from the Connes spectral distance on three types of non compact noncommutative spaces which have received attention recently from various viewpoints in the physics literature. These are the noncommutative Moyal plane, a family of harmonic Moyal spectral triples for which the Dirac operator squares to the harmonic oscillator Hamiltonian and a family of spectral triples with Dirac operator related to the Landau operator. We show that these triples are homothetic spectral metric spaces, having an infinite number of distinct pathwise connected components. The homothetic factors linking the distances are related to determinants of effective Clifford metrics. We obtain as a by product new examples of explicit spectral distance formulas. The results are discussed.Comment: 23 pages. Misprints corrected, references updated, one remark added at the end of the section 3. To appear in Review in Mathematical Physic
    corecore