Editing Renormalization group (section)

===Reformulation===
Meanwhile, the RG in particle physics had been reformulated in more practical terms by Callan and Symanzik in 1970.<ref name=CS>{{cite journal |last=Callan |first=C.G. |year=1970 |title=Broken scale invariance in scalar field theory |doi=10.1103/PhysRevD.2.1541 |journal=Physical Review D |volume=2 |issue=8 |pages=1541–1547 |bibcode=1970PhRvD...2.1541C}}</ref><ref>{{cite journal |last=Symanzik |first=K. |year=1970 |title=Small distance behaviour in field theory and power counting |doi=10.1007/BF01649434 |journal=Communications in Mathematical Physics |volume=18 |issue=3 |pages=227–246 |bibcode=1970CMaPh..18..227S|s2cid=76654566 |url=http://projecteuclid.org/euclid.cmp/1103842537 }}</ref> The above beta function, which describes the "running of the coupling" parameter with scale, was also found to amount to the "canonical trace anomaly", which represents the quantum-mechanical breaking of scale (dilation) symmetry in a field theory.{{efn|Remarkably, the trace anomaly and the running coupling quantum mechanical procedures can themselves induce mass.}} Applications of the RG to particle physics exploded in number in the 1970s with the establishment of the [[Standard Model]].

In 1973,<ref>{{cite journal |first1=D.J. |last1=Gross |first2=F. |last2=Wilczek |year=1973 |title=Ultraviolet behavior of non-Abelian gauge theories |journal=[[Physical Review Letters]] |volume=30 |issue=26 |pages=1343–1346 |doi=10.1103/PhysRevLett.30.1343 |doi-access=free |bibcode=1973PhRvL..30.1343G}}</ref><ref>{{cite journal |first=H.D. |last=Politzer |year=1973 |title=Reliable perturbative results for strong interactions |journal=[[Physical Review Letters]]  |volume=30 |issue=26 |pages=1346–1349 |bibcode=1973PhRvL..30.1346P |doi=10.1103/PhysRevLett.30.1346 |doi-access=free}}</ref> it was discovered that a theory of interacting colored quarks, called [[quantum chromodynamics]], had a negative beta function. This means that an initial high-energy value of the coupling will eventuate a special value of {{mvar|μ}} at which the coupling blows up (diverges). This special value is the [[Strong coupling constant#QCD and asymptotic freedom|scale of the strong interactions]], [[Coupling constant#QCD scale|{{mvar|μ}} = {{math|&Lambda;}}{{sub|QCD}}]] and occurs at about 200 MeV. Conversely, the coupling becomes weak at very high energies ([[asymptotic freedom]]), and the quarks become observable as point-like particles, in [[deep inelastic scattering]], as anticipated by Feynman–Bjorken scaling. QCD was thereby established as the quantum field theory controlling the strong interactions of particles.

Momentum space RG also became a highly developed tool in solid state physics, but was hindered by the extensive use of perturbation theory, which prevented the theory from succeeding in strongly correlated systems.{{efn|For strongly correlated systems, [[Calculus of variations|variational]] techniques are a better alternative.}}