diff options
Diffstat (limited to 'source/know/concept/feynman-diagram')
| -rw-r--r-- | source/know/concept/feynman-diagram/index.md | 15 |
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}}'} |