Topological Graph Polynomials in Colored Group Field Theory

Topological graph polynomials and quantum field theory

We define a new topological polynomial extending the Bollobás-Riordan one, which obeys a four-term reduction relation of the deletion/contraction type and has a natural behavior under partial duality. This allows to write down a completely explicit combinatorial evaluation of the polynomials, occurring in the parametric representation of the non-commutative Grosse-Wulkenhaar quantum field theor...

Topological Graph Polynomials and Quantum Field Theory Part I: Heat Kernel Theories

1) Laboratoire de Physique Théorique, CNRS UMR 8627, Université Paris XI, F-91405 Orsay Cedex, France 2) on leave, Centre de Physique Théorique, CNRS UMR 6207 CNRS Luminy, Case 907, 13288 Marseille Cedex 9 3) Centre de Physique Théorique, CNRS UMR 7644, Ecole Polytechnique F-91128 Palaiseau Cedex, France 4) IFIN, PO Box MG-6, 077125 Magurele, Romania E-mail: [email protected], [email protected]...

A simple proof of orientability in colored group field theory

BACKGROUND Group field theory is an emerging field at the boundary between Quantum Gravity, Statistical Mechanics and Quantum Field Theory and provides a path integral for the gluing of n-simplices. Colored group field theory has been introduced in order to improve the renormalizability of the theory and associates colors to the faces of the simplices. The theory of crystallizations is instead ...

Graph Polynomials and Graph Transformations in Algebraic Graph Theory

The thesis consists of two parts. In the first part we study two graph transformations,namely the Kelmans transformation and the generalized tree shift. In the second part of thisthesis we study an extremal graph theoretic problem and its relationship with algebraic graphtheory. The main results of this thesis are the following. • We show that the Kelmans transformation is a very ef...

Topological Graph Theory A Survey