Skip to content

Commit

Permalink
Add label to s in same footnote
Browse files Browse the repository at this point in the history
  • Loading branch information
niclaurenti committed Jun 3, 2024
1 parent 4428688 commit a108c01
Show file tree
Hide file tree
Showing 2 changed files with 1 addition and 1 deletion.
2 changes: 1 addition & 1 deletion exercises/Ex30.tex
Original file line number Diff line number Diff line change
Expand Up @@ -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 $|f(p_1), \sbar{f}(p_2)\rangle \sim \bcon_{\vp_2,s} \acon_{\vp_1,s} \ket{0}$. 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.
%
Expand Down
Binary file modified main.pdf
Binary file not shown.

0 comments on commit a108c01

Please sign in to comment.