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

* Corresponding author
Abstract : 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 obtain 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 these moments.
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Preprints, Working Papers, ...
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Cited literature [5 references]

https://hal-cea.archives-ouvertes.fr/cea-01280137
Contributor : Emmanuelle de Laborderie <>
Submitted on : Monday, February 29, 2016 - 10:25:37 AM
Last modification on : Wednesday, April 14, 2021 - 12:12:11 PM
Long-term archiving on: : Monday, May 30, 2016 - 3:06:53 PM

### File

1504.00314v2.pdf
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### Identifiers

• HAL Id : cea-01280137, version 1
• ARXIV : 1504.00314

### Citation

Thomas Epelbaum, François Gelis, Bin Wu. From lattice Quantum Electrodynamics to the distribution of the algebraic areas enclosed by random walks on $Z^2$. 2016. ⟨cea-01280137⟩

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