Lesson plan
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\{O_1(\sigma_1) O_2(\sigma_2) \cdots O_N(\sigma_N)\right\} \equiv O_{p_1}(\sigma_{p_1}) O_{p_2}(\sigma_{p_2}) \cdots O_{p_N}(\sigma_{p_N}). Here p is a permutation that orders the parameters by value: : p : \{1, 2, \dots, N\} \to \{1, 2, \dots, N\} : \sigma_{p_1} \leq \sigma_{p_2} \leq \cdots \leq \sigma_{p_N}. For example: : \mathcal P \left\{ O_1(4) O_2(2) O_3(3) O_4(1) \right\} = O_4(1) O_2(2) O_3(3) O_1(4) . In many fields of physics, the most common type of path-ordering is time-ordering, which is discussed in detail below.
Article summary
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\{O_1(\sigma_1) O_2(\sigma_2) \cdots O_N(\sigma_N)\right\} \equiv O_{p_1}(\sigma_{p_1}) O_{p_2}(\sigma_{p_2}) \cdots O_{p_N}(\sigma_{p_N}). Here p is a permutation that orders the parameters by value: : p : \{1, 2, \dots, N\} \to \{1, 2, \dots, N\} : \sigma_{p_1} \leq \sigma_{p_2} \leq \cdots \leq \sigma_{p_N}. For example: : \mathcal P \left\{ O_1(4) O_2(2) O_3(3) O_4(1) \right\} = O_4(1) O_2(2) O_3(3) O_1(4) . In many fields of physics, the most common type of path-ordering is time-ordering, which is discussed in detail below.
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.