Minor rewrites and corrections

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)