From 6e70f28ccbd5afc1506f71f013278a9d157ef03a Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Thu, 27 Oct 2022 20:40:09 +0200
Subject: Optimize last images, add proof template, improve CSS

---
 .../concept/matsubara-greens-function/index.md     | 41 +++++++---------------
 1 file changed, 13 insertions(+), 28 deletions(-)

(limited to 'source/know/concept/matsubara-greens-function')

diff --git a/source/know/concept/matsubara-greens-function/index.md b/source/know/concept/matsubara-greens-function/index.md
index fdcadb3..fd46abf 100644
--- a/source/know/concept/matsubara-greens-function/index.md
+++ b/source/know/concept/matsubara-greens-function/index.md
@@ -83,11 +83,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-<div class="accordion">
-<input type="checkbox" id="proof-period"/>
-<label for="proof-period">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-period">Proof.</label>
+
+{% include proof/start.html id="proof-period" -%}
 First $$\tau \!-\! \tau' < 0$$.
 We insert the argument $$\tau \!-\! \tau' \!+\! \hbar \beta$$,
 and use the cyclic property:
@@ -133,9 +130,8 @@ $$\begin{aligned}
     \\
     &= \pm C_{AB}(\tau \!-\! \tau')
 \end{aligned}$$
+{% include proof/end.html id="proof-period" %}
 
-</div>
-</div>
 
 Due to this limited domain $$\tau \in [-\hbar \beta, \hbar \beta]$$,
 the [Fourier transform](/know/concept/fourier-transform/)
@@ -157,11 +153,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-<div class="accordion">
-<input type="checkbox" id="proof-FT-def"/>
-<label for="proof-FT-def">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-FT-def">Proof.</label>
+
+{% include proof/start.html id="proof-fourier-def" -%}
 We will prove that one is indeed the inverse of the other.
 We demand that the inverse FT of the forward FT of $$C_{AB}(\tau)$$
 is simply $$C_{AB}(\tau)$$ again:
@@ -198,9 +191,8 @@ $$\begin{aligned}
     \\
     &= C_{AB}(\tau)
 \end{aligned}$$
+{% include proof/end.html id="proof-fourier-def" %}
 
-</div>
-</div>
 
 Let us now define the **Matsubara frequencies** $$\omega_n$$
 as a species-dependent subset of $$k_n$$:
@@ -228,11 +220,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-<div class="accordion">
-<input type="checkbox" id="proof-FT-alt"/>
-<label for="proof-FT-alt">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-FT-alt">Proof.</label>
+
+{% include proof/start.html id="proof-fourier-alt" -%}
 We split the integral, shift its limits,
 and use the (anti)periodicity of $$C_{AB}$$:
 
@@ -265,9 +254,8 @@ $$\begin{aligned}
     \\
     &= \frac{1}{2} \big( 1 \pm e^{-i k_n \hbar \beta} \big) \int_{-\hbar \beta}^0 C_{AB}(\tau) \: e^{i k_n \tau} \dd{\tau}
 \end{aligned}$$
+{% include proof/end.html id="proof-fourier-alt" %}
 
-</div>
-</div>
 
 If we actually evaluate this,
 we obtain the following form of $$C_{AB}$$,
@@ -283,11 +271,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-<div class="accordion">
-<input type="checkbox" id="proof-Lehmann"/>
-<label for="proof-Lehmann">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-Lehmann">Proof.</label>
+
+{% include proof/start.html id="proof-lehmann" -%}
 For $$\tau \!-\! \tau' > 0$$, we start by expanding
 in the many-particle eigenstates $$\Ket{n}$$:
 
@@ -363,8 +348,8 @@ $$\begin{aligned}
 \end{aligned}$$
 
 Where swapping $$n$$ and $$n'$$ gives the desired result.
-</div>
-</div>
+{% include proof/end.html id="proof-lehmann" %}
+
 
 This gives us the primary use of the Matsubara Green's function $$C_{AB}$$:
 calculating the retarded $$C_{AB}^R$$ and advanced $$C_{AB}^A$$.
-- 
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