The local renormalization group and its consequences
Abstract: The renormalization scale that has to be introduced in a quantum field theory is usually taken to be identical in all points of space-time. There is however a formalism that allows for a space-time-dependent renormalization scale, with interesting consequences. We highlight three of them: (1) The existence of a function monotonic under the renormalization group flow, establishing the “a theorem” in perturbation theory. (2) Cross-relations among the beta functions of a theory at different loop orders. (3) The possible existence of a new type of solitons.
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