The Ponzano–Regge Model and Parametric Representation
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- 作者：Dan Li (1)
- 刊名：Communications in Mathematical Physics
- 出版年：2014
- 出版时间：April 2014
- 年：2014
- 卷：327
- 期：1
- 页码：243-260
- 全文大小：327 KB
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1. Department of Mathematics, Florida State University, Tallahassee, FL, 32306, USA - ISSN：1432-0916
文摘
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.