From lattice Quantum Electrodynamics to the distribution of the algebraic areas enclosed by random walks on $Z^2$

Autor:	Epelbaum, Thomas, Gelis, Francois, Wu, Bin
Rok vydání:	2015
Předmět:	Mathematical Physics High Energy Physics - Lattice High Energy Physics - Theory Mathematics - Combinatorics
Zdroj:	Annales de l'Institut Henri Poincar\'e D3, 381 (2016)
Druh dokumentu:	Working Paper
DOI:	10.4171/AIHPD/33
Popis:	In the worldline formalism, scalar Quantum Electrodynamics on a 2-dimensional lattice is related to the areas of closed loops on this lattice. We exploit this relationship in order to determine the general structure of the moments of the algebraic areas over the set of loops that have fixed number of edges in the two directions. We show that these moments are the product of a combinatorial factor that counts the number of such loops, by a polynomial in the numbers of steps in each direction. Our approach leads to an algorithm for obtaining explicit formulas for the moments of low order. Comment: 21 pages, to appear in Annales de l'Institut Henri Poincar\'e D
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1504.00314 Zobrazit plný text záznamu View this record from Arxiv