From 4428688138c43ad9466d35610b97db10da9d8f36 Mon Sep 17 00:00:00 2001 From: niccolo Date: Mon, 3 Jun 2024 13:40:42 +0200 Subject: [PATCH] Fix typo in footnote in ex 30 --- exercises/Ex30.tex | 2 +- main.pdf | Bin 736131 -> 736138 bytes 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/exercises/Ex30.tex b/exercises/Ex30.tex index c4784f9..d7153c4 100644 --- a/exercises/Ex30.tex +++ b/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 $|f(p_1), \sbar{f}(p_2)\rangle \sim \acon_{\vp_1,s} \bcon_{\vp_2,s}\ket{0}$ 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 $\psi$. 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. % diff --git a/main.pdf b/main.pdf index 723c5a716123909bd500c8bc90f74fd6aade7ad4..b0a1dae77f2a98648764989e38ee5fd40183779d 100644 GIT binary patch delta 7167 zcmaiWWmFVE+cq7`(kZ2M!_wUil2U?{w6ws|EK4n*ONSzjbT^XA5+dCoxqy^(BO#y9 zd!F|@-@ot2b;coO|w>$Q$1H8{Y6J^d^im>QwX}+?jMV7-HzYt%fuhr#O&? zb8E6}G{;f4bL*|5%|_W$)IrLhTDk7{Kef|dR2SB&u?%0Hq{7VvpVC|Q35FqKh=s!k zQ#szgKeeVvvr!2AE$`Q6cENcT8A3ZNW^x*WKP62%PTOB}pFy>EzNl4eXt3xY%hhiy z{*>@8(=23ZM_*j%6iE>NDY4U8{`?10La_H?=-s<;W$?D&rD~=pEgkHWTGljmDAH*> z^VLTeHsL^$m2}5){X7PNbRCCLWe?X7-S0p%?&3xvo6>i6+71Y{U^+63RJ0S)+)Q*j zzi2z0L$grtZ@@)FAf;>$dT>sD=}0)72t4EtZ(j(lkT=3{Gm?)1E?z|02qZ($rNyug zoDf#{U4ocm@oSUcy)UoJa-VgjA?u4o>=dc2QzS(8gj?n?aG`k7 zhl!SrBC48E=FBHN3q?bwB#p6y<;wa}CS#mHk&fu@wXcfAmC7(XMZnPD1nEq&dZ_*@ zDap6NQVo;85{#F)#O0Z5LsA0%pju5%7=)L~Nj0CP>0<)`_K(@C5I3QL`SH&$11AP-CO)KcU3P-LrB-_RtwLa?Y{^l}K2`w~#Np`Gk;mlY-8r4?P+eK&kyy(KcGR(Vj9WHdl z`c(s?zOahLbs|DcDKWMLL~#ubhot| z-tc^I%;2TpN;pa4q!`2+{

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