From bcae81336764eb6c4cdf0f91e2fe632b625dd8b2 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Sun, 23 Oct 2022 22:18:11 +0200
Subject: Optimize and improve naming of all images in knowledge base
---
source/know/concept/feynman-diagram/boson.avif | Bin 0 -> 3329 bytes
source/know/concept/feynman-diagram/boson.png | Bin 0 -> 4811 bytes
.../know/concept/feynman-diagram/conservation.png | Bin 6878 -> 0 bytes
source/know/concept/feynman-diagram/example.avif | Bin 0 -> 4916 bytes
source/know/concept/feynman-diagram/example.png | Bin 0 -> 6878 bytes
.../concept/feynman-diagram/fermion-heavy.avif | Bin 0 -> 1992 bytes
.../know/concept/feynman-diagram/fermion-heavy.png | Bin 0 -> 3292 bytes
.../concept/feynman-diagram/fermion-light.avif | Bin 0 -> 1955 bytes
.../know/concept/feynman-diagram/fermion-light.png | Bin 0 -> 3226 bytes
source/know/concept/feynman-diagram/freegf.png | Bin 3226 -> 0 bytes
source/know/concept/feynman-diagram/fullgf.png | Bin 3292 -> 0 bytes
source/know/concept/feynman-diagram/impurity.avif | Bin 0 -> 1211 bytes
source/know/concept/feynman-diagram/impurity.png | Bin 0 -> 1727 bytes
source/know/concept/feynman-diagram/index.md | 23 +++++++--------------
.../know/concept/feynman-diagram/interaction.png | Bin 4811 -> 0 bytes
.../know/concept/feynman-diagram/perturbation.png | Bin 1727 -> 0 bytes
16 files changed, 8 insertions(+), 15 deletions(-)
create mode 100644 source/know/concept/feynman-diagram/boson.avif
create mode 100644 source/know/concept/feynman-diagram/boson.png
delete mode 100644 source/know/concept/feynman-diagram/conservation.png
create mode 100644 source/know/concept/feynman-diagram/example.avif
create mode 100644 source/know/concept/feynman-diagram/example.png
create mode 100644 source/know/concept/feynman-diagram/fermion-heavy.avif
create mode 100644 source/know/concept/feynman-diagram/fermion-heavy.png
create mode 100644 source/know/concept/feynman-diagram/fermion-light.avif
create mode 100644 source/know/concept/feynman-diagram/fermion-light.png
delete mode 100644 source/know/concept/feynman-diagram/freegf.png
delete mode 100644 source/know/concept/feynman-diagram/fullgf.png
create mode 100644 source/know/concept/feynman-diagram/impurity.avif
create mode 100644 source/know/concept/feynman-diagram/impurity.png
delete mode 100644 source/know/concept/feynman-diagram/interaction.png
delete mode 100644 source/know/concept/feynman-diagram/perturbation.png
(limited to 'source/know/concept/feynman-diagram')
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diff --git a/source/know/concept/feynman-diagram/impurity.avif b/source/know/concept/feynman-diagram/impurity.avif
new file mode 100644
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diff --git a/source/know/concept/feynman-diagram/impurity.png b/source/know/concept/feynman-diagram/impurity.png
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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/):
-
-
-
+{% 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$$ refers to the [Heisenberg picture](/know/concept/heisenberg-picture/):
-
-
-
+{% include image.html file="fermion-heavy.png" width="60%" alt="Heavy fermion line diagram" %}
$$\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:
-
-
-
+{% 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:
-
-
-
+{% 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)$$:
-
-
-
+{% include image.html file="example.png" width="40%" alt="Example: fermion-fermion interaction" %}
$$\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
diff --git a/source/know/concept/feynman-diagram/interaction.png b/source/know/concept/feynman-diagram/interaction.png
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diff --git a/source/know/concept/feynman-diagram/perturbation.png b/source/know/concept/feynman-diagram/perturbation.png
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index 2e8fbf6..0000000
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