From lattice Quantum Electrodynamics to the distribution of the algebraic areas enclosed by random walks on $Z^2$ - CEA - Commissariat à l’énergie atomique et aux énergies alternatives Access content directly
Journal Articles Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions Year : 2016

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

Abstract

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.
Fichier principal
Vignette du fichier
1504.00314v2.pdf (222.44 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

cea-01280137 , version 1 (29-02-2016)
cea-01280137 , version 2 (19-10-2022)

Identifiers

Cite

Thomas Epelbaum, François Gelis, Bin Wu. From lattice Quantum Electrodynamics to the distribution of the algebraic areas enclosed by random walks on $Z^2$. Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions, 2016, 3, pp.381-404. ⟨10.4171/AIHPD/33⟩. ⟨cea-01280137v1⟩
308 View
75 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More