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diff --git a/source/know/concept/greens-functions/index.md b/source/know/concept/greens-functions/index.md
index 0e53945..ddba2cd 100644
--- a/source/know/concept/greens-functions/index.md
+++ b/source/know/concept/greens-functions/index.md
@@ -25,12 +25,12 @@ except in a special case, see below.
 
 If the two operators are single-particle creation/annihilation operators,
 then we get the **single-particle Green's functions**,
-for which the symbol $G$ is used.
+for which the symbol $$G$$ is used.
 
-The **time-ordered** or **causal Green's function** $G_{\nu \nu'}$ is as follows,
-where $\mathcal{T}$ is the [time-ordered product](/know/concept/time-ordered-product/),
-$\nu$ and $\nu'$ are single-particle states,
-and $\hat{c}_\nu$ annihilates a particle from $\nu$, etc.:
+The **time-ordered** or **causal Green's function** $$G_{\nu \nu'}$$ is as follows,
+where $$\mathcal{T}$$ is the [time-ordered product](/know/concept/time-ordered-product/),
+$$\nu$$ and $$\nu'$$ are single-particle states,
+and $$\hat{c}_\nu$$ annihilates a particle from $$\nu$$, etc.:
 
 $$\begin{aligned}
     \boxed{
@@ -39,15 +39,15 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-The expectation value $\Expval{}$ is
+The expectation value $$\Expval{}$$ is
 with respect to thermodynamic equilibrium.
 This is sometimes in the [canonical ensemble](/know/concept/canonical-ensemble/)
 (for some two-particle Green's functions, see below),
 but usually in the [grand canonical ensemble](/know/concept/grand-canonical-ensemble/),
 since we are adding/removing particles.
-In the latter case, we assume that the chemical potential $\mu$
-is already included in the Hamiltonian $\hat{H}$.
-Explicitly, for a complete set of many-particle states $\Ket{\Psi_n}$, we have:
+In the latter case, we assume that the chemical potential $$\mu$$
+is already included in the Hamiltonian $$\hat{H}$$.
+Explicitly, for a complete set of many-particle states $$\Ket{\Psi_n}$$, we have:
 
 $$\begin{aligned}
     G_{\nu \nu'}(t, t')
@@ -58,8 +58,8 @@ $$\begin{aligned}
 \end{aligned}$$
 
 Arguably more prevalent are
-the **retarded Green's function** $G_{\nu \nu'}^R$
-and the **advanced Green's function** $G_{\nu \nu'}^A$
+the **retarded Green's function** $$G_{\nu \nu'}^R$$
+and the **advanced Green's function** $$G_{\nu \nu'}^A$$
 which are defined like so:
 
 $$\begin{aligned}
@@ -74,16 +74,16 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-Where $\Theta$ is a [Heaviside function](/know/concept/heaviside-step-function/),
-and $[,]_{\mp}$ is a commutator for bosons,
+Where $$\Theta$$ is a [Heaviside function](/know/concept/heaviside-step-function/),
+and $$[,]_{\mp}$$ is a commutator for bosons,
 and an anticommutator for fermions.
 Depending on the context,
 we could either be in the [Heisenberg picture](/know/concept/heisenberg-picture/)
 or in the [interaction picture](/know/concept/interaction-picture/),
-hence $\hat{c}_\nu$ and $\hat{c}_{\nu'}^\dagger$ are time-dependent.
+hence $$\hat{c}_\nu$$ and $$\hat{c}_{\nu'}^\dagger$$ are time-dependent.
 
-Furthermore, the **greater Green's function** $G_{\nu \nu'}^>$
-and **lesser Green's function** $G_{\nu \nu'}^<$ are:
+Furthermore, the **greater Green's function** $$G_{\nu \nu'}^>$$
+and **lesser Green's function** $$G_{\nu \nu'}^<$$ are:
 
 $$\begin{aligned}
     \boxed{
@@ -97,7 +97,7 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-Where $-$ is for bosons, and $+$ for fermions.
+Where $$-$$ is for bosons, and $$+$$ for fermions.
 With this, the causal, retarded and advanced Green's functions
 can thus be expressed as follows:
 
@@ -113,10 +113,10 @@ $$\begin{aligned}
 \end{aligned}$$
 
 If the Hamiltonian involves interactions,
-it might be more natural to use quantum field operators $\hat{\Psi}(\vb{r}, t)$
-instead of choosing a basis of single-particle states $\psi_\nu$.
-In that case, instead of a label $\nu$,
-we use the spin $s$ and position $\vb{r}$, leading to:
+it might be more natural to use quantum field operators $$\hat{\Psi}(\vb{r}, t)$$
+instead of choosing a basis of single-particle states $$\psi_\nu$$.
+In that case, instead of a label $$\nu$$,
+we use the spin $$s$$ and position $$\vb{r}$$, leading to:
 
 $$\begin{aligned}
     G_{ss'}(\vb{r}, t; \vb{r}', t')
@@ -125,14 +125,14 @@ $$\begin{aligned}
     &= \sum_{\nu \nu'} \psi_\nu(\vb{r}) \: \psi^*_{\nu'}(\vb{r}') \: G_{\nu \nu'}(t, t')
 \end{aligned}$$
 
-And analogously for $G_{ss'}^R$, $G_{ss'}^A$, $G_{ss'}^>$ and $G_{ss'}^<$.
-Note that the time-dependence is given to the old $G_{\nu \nu'}$,
-i.e. to $\hat{c}_\nu$ and $\hat{c}_{\nu'}^\dagger$,
+And analogously for $$G_{ss'}^R$$, $$G_{ss'}^A$$, $$G_{ss'}^>$$ and $$G_{ss'}^<$$.
+Note that the time-dependence is given to the old $$G_{\nu \nu'}$$,
+i.e. to $$\hat{c}_\nu$$ and $$\hat{c}_{\nu'}^\dagger$$,
 because we are in the Heisenberg picture.
 
 If the Hamiltonian is time-independent,
 then it can be shown that all the Green's functions
-only depend on the time-difference $t - t'$:
+only depend on the time-difference $$t - t'$$:
 
 $$\begin{gathered}
     G_{\nu \nu'}(t, t') = G_{\nu \nu'}(t - t')
@@ -152,20 +152,20 @@ $$\begin{gathered}
 <div class="hidden" markdown="1">
 <label for="proof-time-diff">Proof.</label>
 We will prove that the thermal expectation value
-$\expval{\hat{A}(t) \hat{B}(t')}$ only depends on $t - t'$
-for arbitrary $\hat{A}$ and $\hat{B}$,
+$$\expval{\hat{A}(t) \hat{B}(t')}$$ only depends on $$t - t'$$
+for arbitrary $$\hat{A}$$ and $$\hat{B}$$,
 and it trivially follows that the Green's functions do too.
 
 In (grand) canonical equilibrium, we know that the
 [density operator](/know/concept/density-operator/)
-$\hat{\rho}$ is as follows:
+$$\hat{\rho}$$ is as follows:
 
 $$\begin{aligned}
     \hat{\rho} = \frac{1}{Z} \exp(- \beta \hat{H})
 \end{aligned}$$
 
 The expected value of the product
-of the time-independent operators $\hat{A}$ and $\hat{B}$ is then:
+of the time-independent operators $$\hat{A}$$ and $$\hat{B}$$ is then:
 
 $$\begin{aligned}
     \expval{\hat{A}(t) \hat{B}(t')}
@@ -175,17 +175,17 @@ $$\begin{aligned}
     e^{i t' \hat{H} / \hbar} \hat{B} e^{-i t' \hat{H} / \hbar} \Big)
 \end{aligned}$$
 
-Using that the trace $\Tr$ is invariant
+Using that the trace $$\Tr$$ is invariant
 under cyclic permutations of its argument,
-and that all functions of $\hat{H}$ commute, we find:
+and that all functions of $$\hat{H}$$ commute, we find:
 
 $$\begin{aligned}
     \expval{\hat{A}(t) \hat{B}(t')}
     = \frac{1}{Z} \Tr\!\Big( e^{-\beta \hat{H}} e^{i (t - t') \hat{H} / \hbar} \hat{A} e^{-i (t - t') \hat{H} / \hbar} \hat{B} \Big)
 \end{aligned}$$
 
-As expected, this only depends on the time difference $t - t'$,
-because $\hat{H}$ is time-independent by assumption.
+As expected, this only depends on the time difference $$t - t'$$,
+because $$\hat{H}$$ is time-independent by assumption.
 Note that thermodynamic equilibrium is crucial:
 intuitively, if the system is not in equilibrium,
 then it evolves in some transient time-dependent way.
@@ -193,11 +193,11 @@ then it evolves in some transient time-dependent way.
 </div>
 
 If the Hamiltonian is both time-independent and non-interacting,
-then the time-dependence of $\hat{c}_\nu$
+then the time-dependence of $$\hat{c}_\nu$$
 can simply be factored out as
-$\hat{c}_\nu(t) = \hat{c}_\nu \exp(- i \varepsilon_\nu t / \hbar)$.
-Then the diagonal ($\nu = \nu'$) greater and lesser Green's functions
-can be written in the form below, where $f_\nu$ is either
+$$\hat{c}_\nu(t) = \hat{c}_\nu \exp(- i \varepsilon_\nu t / \hbar)$$.
+Then the diagonal ($$\nu = \nu'$$) greater and lesser Green's functions
+can be written in the form below, where $$f_\nu$$ is either
 the [Fermi-Dirac distribution](/know/concept/fermi-dirac-distribution/)
 or the [Bose-Einstein distribution](/know/concept/bose-einstein-distribution/).
 
@@ -219,7 +219,7 @@ $$\begin{aligned}
 In the absence of interactions,
 we know from the derivation of
 [equation-of-motion theory](/know/concept/equation-of-motion-theory/)
-that the equation of motion of $G^R(\vb{r}, t; \vb{r}', t')$
+that the equation of motion of $$G^R(\vb{r}, t; \vb{r}', t')$$
 is as follows (neglecting spin):
 
 $$\begin{aligned}
@@ -228,7 +228,7 @@ $$\begin{aligned}
     + \frac{i}{\hbar} \Theta(t \!-\! t') \Expval{\Comm{\comm{\hat{H}_0}{\hat{\Psi}(\vb{r}, t)}}{\hat{\Psi}^\dagger(\vb{r}', t')}}
 \end{aligned}$$
 
-If $\hat{H}_0$ only contains kinetic energy,
+If $$\hat{H}_0$$ only contains kinetic energy,
 i.e. there is no external potential,
 it can be shown that:
 
@@ -243,7 +243,7 @@ $$\begin{aligned}
 <div class="hidden" markdown="1">
 <label for="proof-commH0">Proof.</label>
 In the second quantization,
-the Hamiltonian $\hat{H}_0$ is written like so:
+the Hamiltonian $$\hat{H}_0$$ is written like so:
 
 $$\begin{aligned}
     \hat{H}_0
@@ -289,7 +289,7 @@ $$\begin{aligned}
     \int \psi_\nu^*(\vb{r}') \: \psi_\nu(\vb{r}) \: \nabla^2 \psi_{\nu'}(\vb{r}') \dd{\vb{r}'}
 \end{aligned}$$
 
-We know that the $\psi_\nu$ form a *complete* basis,
+We know that the $$\psi_\nu$$ form a *complete* basis,
 which implies (see [Sturm-Liouville theory](/know/concept/sturm-liouville-theory/)):
 
 $$\begin{aligned}
@@ -307,11 +307,12 @@ $$\begin{aligned}
     &= \frac{\hbar^2}{2 m} \sum_{\nu'} \hat{c}_{\nu'} \nabla^2 \psi_{\nu'}(\vb{r})
     = \frac{\hbar^2}{2 m} \nabla^2 \hat{\Psi}(\vb{r})
 \end{aligned}$$
+
 </div>
 </div>
 
 After substituting this into the equation of motion,
-we recognize $G^R(\vb{r}, t; \vb{r}', t')$ itself:
+we recognize $$G^R(\vb{r}, t; \vb{r}', t')$$ itself:
 
 $$\begin{aligned}
     i \hbar \pdv{G^R}{t}
@@ -342,12 +343,12 @@ i.e. the Hamiltonian only contains kinetic energy.
 
 ## Two-particle functions
 
-We generalize the above to two arbitrary operators $\hat{A}$ and $\hat{B}$,
+We generalize the above to two arbitrary operators $$\hat{A}$$ and $$\hat{B}$$,
 giving us the **two-particle Green's functions**,
 or just **correlation functions**.
-The **causal correlation function** $C_{AB}$,
-the **retarded correlation function** $C_{AB}^R$
-and the **advanced correlation function** $C_{AB}^A$ are defined as follows
+The **causal correlation function** $$C_{AB}$$,
+the **retarded correlation function** $$C_{AB}^R$$
+and the **advanced correlation function** $$C_{AB}^A$$ are defined as follows
 (in the Heisenberg picture):
 
 $$\begin{aligned}
@@ -365,15 +366,15 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-Where the expectation value $\Expval{}$ is taken of thermodynamic equilibrium.
-The name *two-particle* comes from the fact that $\hat{A}$ and $\hat{B}$
+Where the expectation value $$\Expval{}$$ is taken of thermodynamic equilibrium.
+The name *two-particle* comes from the fact that $$\hat{A}$$ and $$\hat{B}$$
 will often consist of a sum of products
 of two single-particle creation/annihilation operators.
 
 Like for the single-particle Green's functions,
 if the Hamiltonian is time-independent,
 then it can be shown that the two-particle functions
-only depend on the time-difference $t - t'$:
+only depend on the time-difference $$t - t'$$:
 
 $$\begin{aligned}
     G_{\nu \nu'}(t, t') = G_{\nu \nu'}(t \!-\! t')