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

Thomas Epelbaum (1) , François Gelis (2) , Bin Wu (3)

1 McGill University = Université McGill [Montréal, Canada]
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681
3 Department of Physics [Columbus]

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.

Domaines: Physique mathématique [math-ph]; Physique des Hautes Energies - Réseau [hep-lat]; Physique des Hautes Energies - Théorie [hep-th]

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⟩