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authorPrefetch2022-10-23 22:18:11 +0200
committerPrefetch2022-10-23 22:18:11 +0200
commitbcae81336764eb6c4cdf0f91e2fe632b625dd8b2 (patch)
treebf353d26203b6792bb2ab5d7bbb5c65819c9e0a0 /source/know/concept/feynman-diagram
parent16555851b6514a736c5c9d8e73de7da7fc9b6288 (diff)
Optimize and improve naming of all images in knowledge base
Diffstat (limited to 'source/know/concept/feynman-diagram')
-rw-r--r--source/know/concept/feynman-diagram/boson.avifbin0 -> 3329 bytes
-rw-r--r--source/know/concept/feynman-diagram/boson.png (renamed from source/know/concept/feynman-diagram/interaction.png)bin4811 -> 4811 bytes
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-rw-r--r--source/know/concept/feynman-diagram/example.png (renamed from source/know/concept/feynman-diagram/conservation.png)bin6878 -> 6878 bytes
-rw-r--r--source/know/concept/feynman-diagram/fermion-heavy.avifbin0 -> 1992 bytes
-rw-r--r--source/know/concept/feynman-diagram/fermion-heavy.png (renamed from source/know/concept/feynman-diagram/fullgf.png)bin3292 -> 3292 bytes
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-rw-r--r--source/know/concept/feynman-diagram/fermion-light.png (renamed from source/know/concept/feynman-diagram/freegf.png)bin3226 -> 3226 bytes
-rw-r--r--source/know/concept/feynman-diagram/impurity.avifbin0 -> 1211 bytes
-rw-r--r--source/know/concept/feynman-diagram/impurity.png (renamed from source/know/concept/feynman-diagram/perturbation.png)bin1727 -> 1727 bytes
-rw-r--r--source/know/concept/feynman-diagram/index.md23
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diff --git a/source/know/concept/feynman-diagram/index.md b/source/know/concept/feynman-diagram/index.md
index c36e7df..ace8dbc 100644
--- a/source/know/concept/feynman-diagram/index.md
+++ b/source/know/concept/feynman-diagram/index.md
@@ -25,6 +25,7 @@ Below, we go through the most notable components of Feynman diagrams
and how to translate them into a mathematical expression.
+
## Real space
The most common component is a **fermion line**, which represents
@@ -37,9 +38,7 @@ Let the subscript $$I$$ refer to the
and $$\mathcal{T}\{\}$$ denote the
[time-ordered product](/know/concept/time-ordered-product/):
-<a href="freegf.png">
-<img src="freegf.png" style="width:60%">
-</a>
+{% include image.html file="fermion-light.png" width="60%" alt="Fermion line diagram" %}
$$\begin{aligned}
= i \hbar G_{s_2 s_1}^0(\vb{r}_2, t_2; \vb{r}_1, t_1)
@@ -59,9 +58,7 @@ Less common is a **heavy fermion line**, representing
a causal Green's function $$G$$ for the entire Hamiltonian $$\hat{H}$$,
where the subscript $$H$$ refers to the [Heisenberg picture](/know/concept/heisenberg-picture/):
-<a href="fullgf.png">
-<img src="fullgf.png" style="width:60%">
-</a>
+{% include image.html file="fermion-heavy.png" width="60%" alt="Heavy fermion line diagram" %}
$$\begin{aligned}
= i \hbar G_{s_2 s_1}(\vb{r}_2, t_2; \vb{r}_1, t_1)
@@ -75,9 +72,7 @@ which we assume to be instantaneous, i.e. time-independent
hence it starts and ends at the same time,
and no arrow is drawn:
-<a href="interaction.png">
-<img src="interaction.png" style="width:60%">
-</a>
+{% include image.html file="boson.png" width="60%" alt="Boson/interaction line diagram" %}
$$\begin{aligned}
= \frac{1}{i \hbar} W_{s_2 s_1}(\vb{r}_2, t_2; \vb{r}_1, t_1)
@@ -99,9 +94,7 @@ $$\begin{aligned}
One-body (time-dependent) operators $$\hat{V}$$ in $$\hat{H}_1$$
are instead represented by a special vertex:
-<a href="perturbation.png">
-<img src="perturbation.png" style="width:35%">
-</a>
+{% include image.html file="impurity.png" width="35%" alt="One-body perturbation (e.g. impurity) diagram" %}
$$\begin{aligned}
= \frac{1}{i \hbar} V_s(\vb{r}, t)
@@ -148,6 +141,7 @@ so that a particle with a given spin propagates
from vertex to vertex without getting flipped.
+
## Fourier space
If the system is time-independent and spatially uniform,
@@ -177,9 +171,7 @@ Working in Fourier space allows us to simplify calculations.
Consider the following diagram and the resulting expression,
where $$\tilde{\vb{r}} = (\vb{r}, t)$$, and $$\tilde{\vb{k}} = (\vb{k}, \omega)$$:
-<a href="conservation.png">
-<img src="conservation.png" style="width:40%">
-</a>
+{% include image.html file="example.png" width="40%" alt="Example: fermion-fermion interaction" %}
$$\begin{aligned}
&= (i \hbar)^3 \sum_{s s'} \!\!\iint \dd{\tilde{\vb{r}}} \dd{\tilde{\vb{r}}'}
@@ -274,6 +266,7 @@ then conservation removes all internal variables,
so no integrals would be needed.
+
## Imaginary time
Feynman diagrams are also useful when working with