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Asymptotic safety (sometimes also referred to as nonperturbative renormalizability) is a concept in quantum field theory which aims at finding a consistent and predictive quantum theory of the gravitational field. Its key ingredient is a nontrivial fixed point of the theory's renormalization group flow which controls the behavior of the coupling constants in the ultraviolet (UV) regime and renders physical quantities safe from divergences. Although originally proposed by Steven Weinberg to find a theory of quantum gravity, the idea of a nontrivial fixed point providing a possible UV completion can be applied also to other field theories, in particular to perturbatively nonrenormalizable ones. In this respect, it is similar to Quantum triviality. The essence of asymptotic safety is the observation that nontrivial renormalization group fixed points can be used to generalize the procedure of perturbative renormalization. In an asymptotically safe theory the couplings do not need to be small or tend to zero in the high energy limit but rather tend to finite values: they approach a nontrivial UV fixed point. The running of the coupling constants, i.e. their scale dependence described by the renormalization group (RG), is thus special in its UV limit in the sense that all their dimensionless combinations remain finite. This suffices to avoid unphysical divergences, e.g. in scattering amplitudes. The requirement of a UV fixed point restricts the form of the bare action and the values of the bare coupling constants, which become predictions of the asymptotic safety program rather than inputs. As for gravity, the standard procedure of perturbative renormalization fails since Newton's constant, the relevant expansion parameter, has negative mass dimension rendering general relativity perturbatively nonrenormalizable. This has driven the search for nonperturbative frameworks describing quantum gravity, including asymptotic safety which — in contrast to other approaches—is characterized by its use of quantum field theory methods, without depending on perturbative techniques, however. At the present time, there is accumulating evidence for a fixed point suitable for asymptotic safety, while a rigorous proof of its existence is still lacking. == Motivation == Gravity, at the classical level, is described by Einstein's field equations of general relativity, . These equations combine the spacetime geometry encoded in the metric with the matter content comprised in the energy–momentum tensor . The quantum nature of matter has been tested experimentally, for instance quantum electrodynamics is by now one of the most accurately confirmed theories in physics. For this reason quantization of gravity seems plausible, too. Unfortunately the quantization cannot be performed in the standard way (perturbative renormalization): Already a simple power-counting consideration signals the perturbative nonrenormalizability since the mass dimension of Newton's constant is . The problem occurs as follows. According to the traditional point of view renormalization is implemented via the introduction of counterterms that should cancel divergent expressions appearing in loop integrals. Applying this method to gravity, however, the counterterms required to eliminate all divergences proliferate to an infinite number. As this inevitably leads to an infinite number of free parameters to be measured in experiments, the program is unlikely to have predictive power beyond its use as a low energy effective theory. It turns out that the first divergences in the quantization of general relativity which cannot be absorbed in counterterms consistently (i.e. without the necessity of introducing new parameters) appear already at one-loop level in the presence of matter fields. At two-loop level the problematic divergences arise even in pure gravity. In order to overcome this conceptual difficulty the development of nonperturbative techniques was required, providing various candidate theories of quantum gravity. For a long time the prevailing view has been that the very concept of quantum field theory — even though remarkably successful in the case of the other fundamental interactions — is doomed to failure for gravity. By way of contrast, the idea of asymptotic safety retains quantum fields as the theoretical arena and instead abandons only the traditional program of perturbative renormalization. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Asymptotic safety in quantum gravity」の詳細全文を読む スポンサード リンク
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