EFFECTIVE FIELD THEORIES
In doing calculations in field theory, one is generally doing integrals. Big problems arise when the lower limit on r integrals is zero, or the upper limit on momentum integrals is infinity. The processes we can study in the lab are limited experimentally by the smallest distances we can probe with the largest momentum transfer we can accomplish! One elegant solution to these difficulties is an effective field theory. Basically, one just cuts off the integrals at a finite lower limit for r and a finite upper limit for momentum or momentum transfer. Obviously this leaves out some part of physics, but that part could only be explored at much higher energies than we could reach in the foreseeable future.

That is, instead of dealing with bare vertices which as you zoom in on them exhibit more and more complex virtual processes at smaller and smaller scales, cover the vertex with a blob and stop at the surface of the blob. The most successful early example of such an approach was Fermi's 1930 theory of β decay, in which the actual weak vertex, which would have had to involve one or more bosons, was replaced by a three-vertex: n → p + e− + bar-νe.

This kind of approach is extremely useful in studying the  phenomenology of fundamental processes. For example, it is not possible to do exact calculations in QCD due to the non-Abelian nature of the field. So basically every calculation in QCD uses some specific effective field theory, adapted to the specific application needed.
ASYMPTOTIC SAFETY!

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.

Steven Weinberg first proposed this idea as a possible approach to a quantum theory of gravity. But, alas, for gravity the standard procedure of perturbative renormalization fails catastrophically 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 standard 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, but a rigorous proof of its existence is still lacking. While this approach should not be counted out, it may turn out to have problems that cannot be solved. [Text mainly from Wikipedia.]



Steven Weinberg and Kenneth Wilson


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