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Optimisation of the exact renormalisation group
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A simple criterion to optimise coarse-grainings for exact renormalisation group equations is given. It is aimed at improving the convergence of approximate solutions of flow equations. The optimisation criterion is generic, as it refers only to the coarse-grained propagator at vanishing field. In physical terms, it is understood as an optimisation condition for amplitude expansions. Alternatively, it can be interpreted as the requirement to move poles of threshold functions away from the physical region. The link to expansions in field amplitudes is discussed as well. Optimal parameters are given explicitly for a variety of different coarse-grainings. As a by-product it is found that the sharp cut-off regulator does not belong to the class of such optimal coarse-grainings, which explains the poor convergence of amplitude expansions based on it.
Forward citations
Cited by 4 Pith papers
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Fermions and the Renormalisation Group at Large N
At large N, fermionic quantum field theories have exact effective actions depending only on flavour-singlet fermion bilinears, making the local potential approximation exact and yielding new conformal fixed points.
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Spectral Functions of Lorentzian Quantum Gravity
Spectral functions for graviton and scalar graviton modes are derived in Lorentzian asymptotically safe quantum gravity via adapted FRG flow equations, yielding normalisable results consistent with infrared effective theory.
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Regulator and gauge dependence of the Abelian gauge coupling in asymptotically safe quantum gravity
The existence of an asymptotically safe UV completion for the Abelian gauge coupling is shown to survive simultaneous variations of the regulator and gauge parameters in certain minimal-sensitivity regions.
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Matter Spectral Functions from Quantum Gravity
Under asymptotically safe quantum gravity, photon and scalar propagators acquire Källén-Lehmann spectral functions that are non-normalizable and change sign in the ultraviolet.
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