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arXiv · 1503.05333

Lattice worldline representation of correlators in a background field

Thomas Epelbaum·Francois Gelis·Bin Wu
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Abstract

We use a discrete worldline representation in order to study the continuum limit of the one-loop expectation value of dimension two and four local operators in a background field. We illustrate this technique in the case of a scalar field coupled to a non-Abelian background gauge field. The first two coefficients of the expansion in powers of the lattice spacing can be expressed as sums over random walks on a d-dimensional cubic lattice. Using combinatorial identities for the distribution of the areas of closed random walks on a lattice, these coefficients can be turned into simple integrals. Our results are valid for an anisotropic lattice, with arbitrary lattice spacings in each direction.

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Thomas Epelbaum, Francois Gelis, Bin Wu. 2015-03-18. Lattice worldline representation of correlators in a background field. https://arxiv.org/abs/1503.05333

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