Topological Graph Polynomial and Quantum Field Theory Part II: Mehler Kernel Theories

• DOI: 10.1007/s00023-011-0087-2
• Publication Date: 2011-03-22T07:07:40Z
• Authors: Thomas Krajewski; Vincent Rivasseau; Fabien Vignes-Tou...
• Keywords: 81T18; Noncommutative geometry; FOS: Physical sciences; Mathematical Physics (math-ph); Partial duality; 01 natural sciences; Graph polynomial; 004; Quantum field theory; 81R60; [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]; 0103 physical sciences; Map; 05C31; Mathematical Physics; 05C10

58 pages, 23 figures, correction in the references and addition of preprint numbers<br/>We define a new topological polynomial extending the Bollobas-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 theory. An explicit solution of the parametric representation for commutative field theories based on the Mehler kernel is also provided.<br/>