%0 Journal Article
%T From lattice Quantum Electrodynamics to the distribution of the algebraic areas enclosed by random walks on $Z^2$
%+ McGill University = Université McGill [Montréal, Canada]
%+ Institut de Physique Théorique - UMR CNRS 3681 (IPHT)
%+ Department of Physics [Columbus]
%A Epelbaum, Thomas
%A Gelis, François
%A Wu, Bin
%Z 19 pages
%< avec comité de lecture
%Z t15/088
%@ 2308-5827
%J Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions
%I European Mathematical Society
%V 3
%P 381–404
%8 2016
%D 2016
%Z 1504.00314
%R 10.4171/AIHPD/33
%Z Mathematics Subject Classication (2010). 05A15
%Z Physics [physics]/Mathematical Physics [math-ph]
%Z Physics [physics]/High Energy Physics - Lattice [hep-lat]
%Z Physics [physics]/High Energy Physics - Theory [hep-th]Journal articles
%X In theworldline 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.
%G English
%2 https://cea.hal.science/cea-01280137v1/document
%2 https://cea.hal.science/cea-01280137v1/file/1504.00314v2.pdf
%L cea-01280137
%U https://cea.hal.science/cea-01280137