Three-loop calculation of the random walk problem: an application of dimensional transformation and the uniqueness method

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Abstract
The method and details of the calculation of the three-loop contribution to the anomalous dimension of the diffusion coefficient of the model of a random walk in a potential random field with long-range correlations are presented. Contrary to earlier conjectures, this contribution does not vanish identically. A new method of calculation of multi-loop Feynman graphs with complicated numerator structure is suggested. It leads to simpler integrals in a space of higher dimensionality, which are computed using the recursion relations of the uniqueness method.