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Communications in Mathematical Physics

, Volume 327, Issue 1, pp 243–260 | Cite as

The Ponzano–Regge Model and Parametric Representation

Article

Abstract

We give a parametric representation of the effective noncommutative field theory derived from a \({\kappa}\) -deformation of the Ponzano–Regge model and define a generalized Kirchhoff polynomial with \({\kappa}\) -correction terms, obtained in a \({\kappa}\) -linear approximation. We then consider the corresponding graph hypersurfaces and the question of how the presence of the correction term affects their motivic nature. We look in particular at the tetrahedron graph, which is the basic case of relevance to quantum gravity. With the help of computer calculations, we verify that the number of points over finite fields of the corresponding hypersurface does not fit polynomials with integer coefficients, hence the hypersurface of the tetrahedron is not polynomially countable. This shows that the correction term can change significantly the motivic properties of the hypersurfaces, with respect to the classical case.

Keywords

Span Tree Parametric Representation Star Product Multiple Zeta Grothendieck Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsFlorida State UniversityTallahasseeUSA

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