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-rw-r--r--source/know/concept/feynman-diagram/index.md15
1 files changed, 10 insertions, 5 deletions
diff --git a/source/know/concept/feynman-diagram/index.md b/source/know/concept/feynman-diagram/index.md
index ace8dbc..1f1c957 100644
--- a/source/know/concept/feynman-diagram/index.md
+++ b/source/know/concept/feynman-diagram/index.md
@@ -38,7 +38,8 @@ Let the subscript $$I$$ refer to the
and $$\mathcal{T}\{\}$$ denote the
[time-ordered product](/know/concept/time-ordered-product/):
-{% include image.html file="fermion-light.png" width="60%" alt="Fermion line diagram" %}
+{% include image.html file="fermion-light.png" width="60%"
+ alt="Fermion line diagram" %}
$$\begin{aligned}
= i \hbar G_{s_2 s_1}^0(\vb{r}_2, t_2; \vb{r}_1, t_1)
@@ -58,7 +59,8 @@ Less common is a **heavy fermion line**, representing
a causal Green's function $$G$$ for the entire Hamiltonian $$\hat{H}$$,
where the subscript $$H$$ refers to the [Heisenberg picture](/know/concept/heisenberg-picture/):
-{% include image.html file="fermion-heavy.png" width="60%" alt="Heavy fermion line diagram" %}
+{% include image.html file="fermion-heavy.png" width="60%"
+ alt="Heavy fermion line diagram" %}
$$\begin{aligned}
= i \hbar G_{s_2 s_1}(\vb{r}_2, t_2; \vb{r}_1, t_1)
@@ -72,7 +74,8 @@ which we assume to be instantaneous, i.e. time-independent
hence it starts and ends at the same time,
and no arrow is drawn:
-{% include image.html file="boson.png" width="60%" alt="Boson/interaction line diagram" %}
+{% include image.html file="boson.png" width="60%"
+ alt="Boson/interaction line diagram" %}
$$\begin{aligned}
= \frac{1}{i \hbar} W_{s_2 s_1}(\vb{r}_2, t_2; \vb{r}_1, t_1)
@@ -94,7 +97,8 @@ $$\begin{aligned}
One-body (time-dependent) operators $$\hat{V}$$ in $$\hat{H}_1$$
are instead represented by a special vertex:
-{% include image.html file="impurity.png" width="35%" alt="One-body perturbation (e.g. impurity) diagram" %}
+{% include image.html file="impurity.png" width="35%"
+ alt="One-body perturbation (e.g. impurity) diagram" %}
$$\begin{aligned}
= \frac{1}{i \hbar} V_s(\vb{r}, t)
@@ -171,7 +175,8 @@ Working in Fourier space allows us to simplify calculations.
Consider the following diagram and the resulting expression,
where $$\tilde{\vb{r}} = (\vb{r}, t)$$, and $$\tilde{\vb{k}} = (\vb{k}, \omega)$$:
-{% include image.html file="example.png" width="40%" alt="Example: fermion-fermion interaction" %}
+{% include image.html file="example.png" width="40%"
+ alt="Example: fermion-fermion interaction" %}
$$\begin{aligned}
&= (i \hbar)^3 \sum_{s s'} \!\!\iint \dd{\tilde{\vb{r}}} \dd{\tilde{\vb{r}}'}