C-theorem: Difference between revisions

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For this reason, the analog of the ''C''-theorem in four dimensions is called the '''''A''-theorem'''.

In perturbation theory, that is for renormalization flows which do not deviate much from free theories, the ''A''-theorem in four dimensions was proved by [[Hugh Osborn]] <ref>{{cite journal | last1 = Osborn | first1 = Hugh | year = 1989 | title = Derivation of a Four-Dimensional c Theorem | journal = Physics Letters B | volume = 222 | issue = 1| pages = 97 | doi=10.1016/0370-2693(89)90729-6|bibcode =1989PhLB..222...97O }}

{{cite journal | last1 = Ian | first1 = Jack| last2 = Osborn | first2 = Hugh | year = 1990 | title = Analogs for the c Theorem for Four-Dimensional Renormalizable Field Theories | url = http://cds.cern.ch/record/205908| journal = Nuclear Physics B | volume = 343 | issue = 3| pages = 647–688 | doi=10.1016/0550-3213(90)90584-Z|bibcode =1990NuPhB.343..647J }}

</ref> using the local renormalization group equation. However, the problem of finding a proof valid beyond perturbation theory remained open for many years.