Scale Invariance in Quantum Field Theory
The scale-dependence of a quantum field theory (QFT) is characterised by the way its coupling parameters depend on the energy-scale of a given physical process. This energy dependence is described by the renormalization group, and is encoded in the beta-functions of the theory.
For a QFT to be scale-invariant, its coupling parameters must be independent of the energy-scale, and this is indicated by the vanishing of the beta-functions of the theory. Such theories are also known as fixed points of the corresponding renormalization group flow.
Read more about this topic: Scale Invariance
Famous quotes containing the words scale, quantum, field and/or theory:
“... the meanest life, the poorest existence, is attributed to God’s will, but as human beings become more affluent, as their living standard and style begin to ascend the material scale, God descends the scale of responsibility at a commensurate speed.”
—Maya Angelou (b. 1928)
“The receipt to make a speaker, and an applauded one too, is short and easy.—Take of common sense quantum sufficit, add a little application to the rules and orders of the House, throw obvious thoughts in a new light, and make up the whole with a large quantity of purity, correctness, and elegancy of style.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Mothers seem to be in subtle competition with teachers. There is always an underlying fear that teachers will do a better job than they have done with their child.... But mostly mothers feel that their areas of competence are very much similar to those of the teacher. In fact they feel they know their child better than anyone else and that the teacher doesn’t possess any special field of authority or expertise.”
—Sara Lawrence Lightfoot (20th century)
“The theory of the Communists may be summed up in the single sentence: Abolition of private property.”
—Karl Marx (1818–1883)