Scaling dimension

Résumé

In theoretical physics, the scaling dimension, or simply dimension, of a local operator in a quantum field theory characterizes the rescaling properties of the operator under spacetime dilations x\to \lambda x. If the quantum field theory is scale invariant, scaling dimensions of operators are fixed numbers, otherwise they are functions of the distance scale. Scale-invariant quantum field theory In a scale invariant quantum field theory, by definition each operator O acquires under a dilation x\to \lambda x a factor \lambda^{-\Delta}, where \Delta is a number called the scaling dimension of O. This implies in particular that the two point correlation function \langle O(x) O(0)\rangle depends on the distance as (x^2)^{-\Delta}. More generally, correlation functions of several local operators must depend on the distances in such a way that \langle O_1(\lambda x_1) O_2(\lambda x_2)\ldots\rang

Source officielle

https://en.wikipedia.org/wiki/Scaling_dimension

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