Merge branch 'main' of github.com:niclaurenti/QFT_exercises

.github/workflows/upload.yml

@@ -0,0 +1,42 @@
+name: Deploy PDF
+
+on:
+  push:
+    branches:
+      - main
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+
+    steps:
+      - name: Checkout code
+        uses: actions/checkout@v2
+
+      - name: Install LaTeX
+        run: |
+          sudo apt-get update
+          sudo apt-get install -y texlive-full
+
+      - name: Compile LaTeX to PDF
+        run: make
+
+      - name: Clone niclaurenti.github.io
+        uses: actions/checkout@v2
+        with:
+          repository: niclaurenti/niclaurenti.github.io
+          token: ${{ secrets.NICLAURENTI_TOKEN }}
+          path: niclaurenti.github.io
+
+      - name: Copy main.pdf
+        run: |
+            cp main.pdf niclaurenti.github.io/files/qft_exercises.pdf
+    
+      - name: Commit and Push Changes
+        run: |
+          cd niclaurenti.github.io
+          git config user.email "[email protected]"
+          git config user.name "niclaurenti"
+          git add files/qft_exercises.pdf
+          git commit -m "Automated update of qft_exercises.pdf: ${{ github.event.head_commit.message }}"
+          git push

Makefile

@@ -1,2 +1,3 @@
 default:
 	pdflatex main.tex
+	pdflatex main.tex

exercises/Ex2.tex

@@ -61,7 +61,7 @@
 		\begin{split}
 			\phi(t,\vx) & = \int \frac{\rmd^{3} \vp}{(2\pi)^{3}} \big( A(\vp) \, e^{-i \Ep t + i \vp \cdot \vx} + B(\vp) \, e^{i \Ep t + i \vp \cdot \vx} \big)
 			\\
-			& = \int \frac{d^{3} \vp}{(2\pi)^{3}} \big( A(\vp) \, e^{-i \Ep t + i \vp \cdot \vx} + B(-\vp) \, e^{i \Ep t - i \vp \cdot \vx} \big) \,,
+			& = \int \frac{\rmd^{3} \vp}{(2\pi)^{3}} \big( A(\vp) \, e^{-i \Ep t + i \vp \cdot \vx} + B(-\vp) \, e^{i \Ep t - i \vp \cdot \vx} \big) \,,
 		\end{split}
 	\end{equation}
 	where in the second line we replaced the variable of integration as $\vp \mapsto - \vp$. 

exercises/Ex30.tex

@@ -92,7 +92,7 @@
 		\end{tikzpicture} ~ = ~ i\mathcal{M}_s - i\mathcal{M}_u \, .
 	\end{align}
     Observe that the two diagrams have a difference of a minus sign
-    since in Eq.~\eqref{u_contraction} we moved $\sbar{\psi}(x)$ of two spaces to the right, while $\psi(x)$ must be moved of one space to the right, so we are left with a minus sign.  The reason why also $\psi(x)$ must be moved is that all the external state contractions must be done in the same order\footnote{this is related to the fact that we can define $|f(p_1), \sbar{f}(p_2)\rangle \sim \acon_{\vp_1,s} \bcon_{\vp_2,s}\ket{0}$ or $|f(p_1), \sbar{f}(p_2)\rangle \sim \bcon_{\vp_1,s} \acon_{\vp_2,s} \ket{0}$. Both definitions are possible but differ by a minus sign.}: in Eq.~\eqref{s_contraction} we applied to the final particles first $\sbar{\psi}$ and then $\psi$.
+    since in Eq.~\eqref{u_contraction} we moved $\sbar{\psi}(x)$ of two spaces to the right, while $\psi(x)$ must be moved of one space to the right, so we are left with a minus sign.  The reason why also $\psi(x)$ must be moved is that all the external state contractions must be done in the same order\footnote{this is related to the fact that we can define $|f(p_1), \sbar{f}(p_2)\rangle \sim \acon_{\vp_1,s_1} \bcon_{\vp_2,s_2}\ket{0}$ or $|f(p_1), \sbar{f}(p_2)\rangle \sim \bcon_{\vp_2,s_2} \acon_{\vp_1,s_1} \ket{0}$. Both definitions are possible but differ by a minus sign.}: in Eq.~\eqref{s_contraction} we applied to the final particles first $\sbar{\psi}$ and then $\psi$.
     However, in Eq.~\eqref{u_contraction} the fields are placed in the opposite order.
     Therefore, in order to be consistent with the choice done in Eq.~\eqref{s_contraction}, we have to exchange $\psi(x)$ and $\sbar{\psi}(y)$, getting an extra minus sign.
     %