diff options
Diffstat (limited to 'content/know/concept/feynman-diagram/index.pdc')
| -rw-r--r-- | content/know/concept/feynman-diagram/index.pdc | 7 |
1 files changed, 4 insertions, 3 deletions
diff --git a/content/know/concept/feynman-diagram/index.pdc b/content/know/concept/feynman-diagram/index.pdc index dfb63c1..600be61 100644 --- a/content/know/concept/feynman-diagram/index.pdc +++ b/content/know/concept/feynman-diagram/index.pdc @@ -284,12 +284,12 @@ involving the [Matsubara Green's function](/know/concept/matsubara-greens-functi $$\begin{aligned} i \hbar G_{s_2 s_1}^0(\vb{r}_2, t_2; \vb{r}_1, t_1) \:\: &\longrightarrow \:\: - -\!\hbar G_{s_2 s_1}^0(\vb{r}_2, \tau_2; \vb{r}_1, \tau_1) + \hbar G_{s_2 s_1}^0(\vb{r}_2, \tau_2; \vb{r}_1, \tau_1) = \expval{\mathcal{T} \Big\{ \hat{\Psi}_I(\vb{r}_2, \tau_2) \hat{\Psi}_I^\dagger(\vb{r}_1, \tau_1) \Big\}} \\ i \hbar G_{s_2 s_1}(\vb{r}_2, t_2; \vb{r}_1, t_1) \:\: &\longrightarrow \:\: - -\!\hbar G_{s_2 s_1}(\vb{r}_2, \tau_2; \vb{r}_1, \tau_1) + \hbar G_{s_2 s_1}(\vb{r}_2, \tau_2; \vb{r}_1, \tau_1) = \expval{\mathcal{T} \Big\{ \hat{\Psi}_H(\vb{r}_2, \tau_2) \hat{\Psi}_H^\dagger(\vb{r}_1, \tau_1) \Big\}} \end{aligned}$$ @@ -312,7 +312,8 @@ and a distinction must be made between fermionic Matsubara frequencies $i \omega_n^f$ (for $G$ and $G^0$) and bosonic Matsubara ones $i \omega_n^b$ (for $W$). This distinction is compatible with frequency conservation, -since a sum of two fermionic frequencies is always bosonic: +since a sum of two fermionic frequencies is always bosonic. +We have: $$\begin{aligned} G_{s_2 s_1}^0(\vb{r}_2, \tau_2; \vb{r}_1, \tau_1) |