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Path-ordering
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Path-ordering : ウィキペディア英語版
Path-ordering

In theoretical physics, path-ordering is the procedure (or a meta-operator \mathcal P) that orders a product of operators according to the value of a chosen parameter:
:\mathcal P \left\
\equiv O_(\sigma_) O_(\sigma_) \cdots O_(\sigma_).
Here ''p'' is a permutation that orders the parameters by value:
:p \mathrel \ \to \
:\sigma_ \leq \sigma_ \leq \cdots \leq \sigma_.
For example:
:\mathcal P \left\ = O_4(1) O_2(2) O_3(3) O_1(4) .
== Examples ==

If an operator is not simply expressed as a product, but as a function of another operator, we must first perform a Taylor expansion of this function. This is the case of the Wilson loop, which is defined as a path-ordered exponential to guarantee that the Wilson loop encodes the holonomy of the gauge connection. The parameter ''σ'' that determines the ordering is a parameter describing the contour, and because the contour is closed, the Wilson loop must be defined as a trace in order to be gauge-invariant.

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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