Article

Noncommutative Geometry as a Regulator

Physical review D: Particles and fields (Impact Factor: 4.86). 03/2000; 63(2). DOI: 10.1103/PhysRevD.63.025004
Source: arXiv

ABSTRACT

We give a perturbative quantization of space-time $R^4$ in the case where the commutators $C^{{\mu}{\nu}}=[X^{\mu},X^{\nu}]$ of the underlying algebra generators are not central . We argue that this kind of quantum space-times can be used as regulators for quantum field theories . In particular we show in the case of the ${\phi}^4$ theory that by choosing appropriately the commutators $C^{{\mu}{\nu}}$ we can remove all the infinities by reproducing all the counter terms . In other words the renormalized action on $R^4$ plus the counter terms can be rewritten as only a renormalized action on the quantum space-time $QR^4$ . We conjecture therefore that renormalization of quantum field theory is equivalent to the quantization of the underlying space-time $R^4$ . Comment: Latex, 30 pages, no figures,typos corrected,references added . Substantial amount of rewriting of the last section . Final interesting remarks added at the end of the paper

Download full-text

Full-text

Available from: Badis Ydri, Oct 07, 2015
  • Source
    • "Assuming the formula (see e.g. [4], [5]) [1] [ x µ , x ν ] = θ µν ( x) = θ "
    [Show abstract] [Hide abstract]
    ABSTRACT: The star product technique translates the framework of local fields on noncommutative space-time into nonlocal fields on standard space-time. We consider the example of fields on $\kappa$- deformed Minkowski space, transforming under $\kappa$-deformed Poincar\'{e} group with noncommutative parameters. By extending the star product to the tensor product of functions on $\kappa$-deformed Minkowski space and $\kappa$-deformed Poincar\'{e} group we represent the algebra of noncommutative parameters of deformed relativistic symmetries by functions on classical Poincar\'{e} group. Comment: LaTeX2e, 10 pages. To appear in the Proceedings of XXIII International Colloquium on Group-Theoretical Methods in Physics, July 31- August 5, Dubna, Russia". The names of the authors corrected
    Full-text · Article · Dec 2000 · Physics of Atomic Nuclei
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: BFYM on commutative and noncommutative ${\mathbb{R}}^4$ is considered and a Seiberg-Witten gauge-equivalent transformation is constructed for these theories. Then we write the noncommutative action in terms of the ordinary fields and show that it is equivalent to the ordinary action up to higher dimensional gauge invariant terms.
    Full-text · Article · May 2000
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a "fuzzy manifold'. Such discretization by quantization is remarkably successful in preserving symmetries and topological features, and altogether overcoming the fermion-doubling problem. In this thesis, the fuzzification of coadjoint orbits and their QFT's are put forward.
    Preview · Article · Jan 2001
Show more