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 �xed 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.
Accepté le :
Publié le :
DOI : 10.4171/aihpd/33
Publié le :
DOI : 10.4171/aihpd/33
Classification :
05-XX, 81-XX
Mots-clés : Random walks on $\mathbf Z^2$, algebraic areas, lattice quantum electrodynamics
Mots-clés : Random walks on $\mathbf Z^2$, algebraic areas, lattice quantum electrodynamics
@article{AIHPD_2016__3_4_381_0, author = {Epelbaum, Thomas and Gelis, Fran\c{c}ois and Wu, Bin}, title = {From lattice {Quantum} {Electrodynamics} to the distribution of the algebraic areas enclosed by random walks on $\mathbf Z^2$}, journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D}, pages = {381--404}, volume = {3}, number = {4}, year = {2016}, doi = {10.4171/aihpd/33}, zbl = {1386.60163}, language = {en}, url = {http://archive.numdam.org/articles/10.4171/aihpd/33/} }
TY - JOUR AU - Epelbaum, Thomas AU - Gelis, François AU - Wu, Bin TI - From lattice Quantum Electrodynamics to the distribution of the algebraic areas enclosed by random walks on $\mathbf Z^2$ JO - Annales de l’Institut Henri Poincaré D PY - 2016 SP - 381 EP - 404 VL - 3 IS - 4 UR - http://archive.numdam.org/articles/10.4171/aihpd/33/ DO - 10.4171/aihpd/33 LA - en ID - AIHPD_2016__3_4_381_0 ER -
%0 Journal Article %A Epelbaum, Thomas %A Gelis, François %A Wu, Bin %T From lattice Quantum Electrodynamics to the distribution of the algebraic areas enclosed by random walks on $\mathbf Z^2$ %J Annales de l’Institut Henri Poincaré D %D 2016 %P 381-404 %V 3 %N 4 %U http://archive.numdam.org/articles/10.4171/aihpd/33/ %R 10.4171/aihpd/33 %G en %F AIHPD_2016__3_4_381_0
Epelbaum, Thomas; Gelis, François; Wu, Bin. From lattice Quantum Electrodynamics to the distribution of the algebraic areas enclosed by random walks on $\mathbf Z^2$. Annales de l’Institut Henri Poincaré D, Tome 3 (2016) no. 4, pp. 381-404. doi : 10.4171/aihpd/33. http://archive.numdam.org/articles/10.4171/aihpd/33/
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