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http://arxiv.org/abs/1012.3081
The Universal RG Machine
Dario Benedetti, Kai Groh, Pedro F. Machado, Frank Saueressig
38 pages
(Submitted on 14 Dec 2010)
"Functional Renormalization Group Equations constitute a powerful tool to encode the perturbative and non-perturbative properties of a physical system. We present an algorithm to systematically compute the expansion of such flow equations in a given background quantity specified by the approximation scheme. The method is based on off-diagonal heat-kernel techniques and can be implemented on a computer algebra system, opening access to complex computations in, e.g., Gravity or Yang-Mills theory. In a first illustrative example, we re-derive the gravitational beta-functions of the Einstein-Hilbert truncation, demonstrating their background-independence. As an additional result, the heat-kernel coefficients for transverse vectors and transverse-traceless symmetric matrices are computed to second order in the curvature."
This has considerable importance. It makes the Asymptotic Safe QG approach much more viable and opens the way to rapid progress.
The Universal RG Machine
Dario Benedetti, Kai Groh, Pedro F. Machado, Frank Saueressig
38 pages
(Submitted on 14 Dec 2010)
"Functional Renormalization Group Equations constitute a powerful tool to encode the perturbative and non-perturbative properties of a physical system. We present an algorithm to systematically compute the expansion of such flow equations in a given background quantity specified by the approximation scheme. The method is based on off-diagonal heat-kernel techniques and can be implemented on a computer algebra system, opening access to complex computations in, e.g., Gravity or Yang-Mills theory. In a first illustrative example, we re-derive the gravitational beta-functions of the Einstein-Hilbert truncation, demonstrating their background-independence. As an additional result, the heat-kernel coefficients for transverse vectors and transverse-traceless symmetric matrices are computed to second order in the curvature."
This has considerable importance. It makes the Asymptotic Safe QG approach much more viable and opens the way to rapid progress.