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scaling dimension : ウィキペディア英語版
scaling dimension
In theoretical physics, scaling dimension, or simply dimension, of a local operator in a quantum field theory characterizes 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 depending on the distance scale.
== Scale invariant quantum field theory ==

In a scale invariant quantum field theory, by definition each operator ''O'' acquires under a dilatation x\to \lambda x a factor \lambda^, 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)^. 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\rangle=
\lambda^\langle O_1(x_1) O_2(x_2)\ldots\rangle

It should be noted that most scale invariant theories are also conformally invariant, which imposes further constraints on correlation functions of local operators.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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