Migrate from 'jekyll-katex' to 'kramdown-math-sskatex'

1 files changed, 15 insertions, 15 deletions

diff --git a/source/know/concept/time-ordered-product/index.md b/source/know/concept/time-ordered-product/index.md
index eab92ff..e414ccf 100644
--- a/source/know/concept/time-ordered-product/index.md
+++ b/source/know/concept/time-ordered-product/index.md
@@ -14,8 +14,8 @@ explicitly time-dependent operators,
 subject to certain ordering constraints.
 
 Let us start with an unusual motivation.
-Suppose that some time-dependent operator $\hat{A}(t)$ is defined like so,
-as a product of $N$ time-dependent sub-operators $\hat{a}_n(t)$:
+Suppose that some time-dependent operator $$\hat{A}(t)$$ is defined like so,
+as a product of $$N$$ time-dependent sub-operators $$\hat{a}_n(t)$$:
 
 $$\begin{aligned}
     \hat{A}(t)
@@ -27,17 +27,17 @@ Crucially, the upper limits of the inner integrals
 depend on the surrounding variables,
 meaning that these integrals cannot simply be reordered.
 
-An interpretation is that the rightmost $\hat{a}_N(t_N)$ is applied first,
-and then $\hat{a}_{N-1}(t_{N-1})$ secondly with $t_{N-1} > t_N$,
+An interpretation is that the rightmost $$\hat{a}_N(t_N)$$ is applied first,
+and then $$\hat{a}_{N-1}(t_{N-1})$$ secondly with $$t_{N-1} > t_N$$,
 and so on.
 This suggests there is a form of "time-ordering" here:
-the integrals sweep across all relative timings of $\hat{a}_n$,
+the integrals sweep across all relative timings of $$\hat{a}_n$$,
 but preserve the ordering.
 Indeed, this could be rewritten as a time-ordered product
 (see the [interaction picture](/know/concept/interaction-picture/) for an example).
 
 A more general and intuitive motivation goes as follows.
-Suppose we have a product of $N$ time-dependent operators $\hat{a}_n(t)$,
+Suppose we have a product of $$N$$ time-dependent operators $$\hat{a}_n(t)$$,
 each representing a certain event.
 Clearly, we would want to apply them in chronological order:
 
@@ -47,10 +47,10 @@ $$\begin{aligned}
     t_N > t_{N-1} > ... > \: t_2 > t_1
 \end{aligned}$$
 
-But what if the ordering of the arguments $t_N, ..., t_1$
+But what if the ordering of the arguments $$t_N, ..., t_1$$
 is not known in advance?
-We thus define the **time-ordering meta-operator** $\mathcal{T}$,
-which reorders the operators based on the $t$-values
+We thus define the **time-ordering meta-operator** $$\mathcal{T}$$,
+which reorders the operators based on the $$t$$-values
 such that they are always in chronological order.
 For example:
 
@@ -63,13 +63,13 @@ $$\begin{aligned}
     \end{cases}
 \end{aligned}$$
 
-This example suggests a general algorithm for $\mathcal{T}$:
-we need to consider every permutation of the operators $\hat{a}_n(t_n)$,
+This example suggests a general algorithm for $$\mathcal{T}$$:
+we need to consider every permutation of the operators $$\hat{a}_n(t_n)$$,
 and leave only the single one that satisfies our demands.
 
 Mathematically, we do this by summing up all permutations,
 and multiplying each term with a product of
-[Heaviside step functions](/know/concept/heaviside-step-function/) $\Theta$,
+[Heaviside step functions](/know/concept/heaviside-step-function/) $$\Theta$$,
 which remove the term if the ordering is wrong:
 
 $$\begin{aligned}
@@ -79,7 +79,7 @@ $$\begin{aligned}
     \: \hat{a}_{p_1}(t_{p_1}) \: \cdots \: \hat{a}_{p_N}(t_{p_N})
 \end{aligned}$$
 
-With this, our earlier example for two operators $\hat{a}_1$ and $\hat{a}_2$
+With this, our earlier example for two operators $$\hat{a}_1$$ and $$\hat{a}_2$$
 takes the following form:
 
 $$\begin{aligned}
@@ -99,8 +99,8 @@ $$\begin{aligned}
     = \Theta(t_1 - t_2) \: \hat{a}_1(t_1) \: \hat{a}_2(t_2) \pm \Theta(t_2 - t_1) \: \hat{a}_2(t_2) \: \hat{a}_1(t_1)
 \end{aligned}$$
 
-Where $\pm$ is $+$ for bosons, and $-$ for fermions in this case.
-The general definition of $\mathcal{T}$ is:
+Where $$\pm$$ is $$+$$ for bosons, and $$-$$ for fermions in this case.
+The general definition of $$\mathcal{T}$$ is:
 
 $$\begin{aligned}
     \boxed{