There are actually two things I wanted to address. The first shows up on page 16 of the pdf. I think I recall seeing somewhere that there is a way to code to print across a natural page break? I think this is why the equations are blocking up like this. If not, I can break it up manually, if I have to. Just checking.
The other thing is essentially an opinion. I had to break the lines of the equations up; it's QFT, the equations sometimes just get long. (For example, again please see page 16.) There are a zillion ways to break up a line, and this one doesn't look half bad. Aesthetically speaking, does anyone have suggestions how I might be able to make this look a bit more professional? And, before anyone asks, yes I would like to keep all those steps!
(Sorry, I can't figure out how to get the packages to load properly. I've really got to learn how to do that! I've provided some of the code merely for completeness and if anyone wants to try any edits to show me something. I don't know how it would look printed out: it's just a collection of the coding without any of the text to go with it. I split the lines of the equations using arrays. I couldn't get aligned to look right because the first line just covered too much of the line.)
Thanks for any suggestions!
-Dan
Code: Select all
Code, edit and compile here:
$\begin{equation}\begin{array}{l}{\displaystyle \int\dfrac{d^{\,4}q}{(2\pi^{4})\sqrt{2q_{0}}}\,\bigg(A_{4}^{\nu*}(\textbf{k}_{4})(2\pi)^{4}G\gamma^{\nu}\delta^{4}(q+k_{2}-k_{4})A_{2}^{\nu}(\textbf{k}_{2})\bigg)\dfrac{-i}{(2\pi)^{4}}\dfrac{1}{\sqrt{\textbf{q}^{2}-m^{2}}}}\\\hphantom{XXXX}\times\bigg(A_{3}^{\mu*}(\textbf{k}_{3})(2\pi)^{4}G\gamma^{\mu}\delta^{4}(k_{1}-q-k_{3})A_{1}^{\mu}(\textbf{k}_{1})\bigg)\end{array}\end{equation}$$\begin{equation}\begin{array}{l}{\displaystyle \int\dfrac{d^{\,4}q}{(2\pi^{4})\sqrt{2q_{0}}}\,\bigg(A_{4}^{\nu*}(\textbf{k}_{3})(2\pi)^{4}G\gamma^{\nu}\delta^{4}(q+k_{2}-k_{3})A_{2}^{\nu}(\textbf{k}_{2})\bigg)\dfrac{-i}{(2\pi)^{4}}\dfrac{1}{\sqrt{\textbf{q}^{2}-m^{2}}}}\\\hphantom{XXXX}\times\bigg(A_{4}^{\mu*}(\textbf{k}_{4})(2\pi)^{4}G\gamma^{\mu}\delta^{4}(k_{1}-q-k_{3})A_{1}^{\mu}(\textbf{k}_{1})\bigg)\end{array}\end{equation}$$\begin{equation}\begin{array}{l}{\displaystyle \int\dfrac{d^{\,4}q}{(2\pi)^{4}\sqrt{2q_{0}}}[\overline{u}_{4}(2\pi)^{4}ie\gamma^{\nu}\delta^{4}(q+p_{2}-p_{4})u_{2}]\dfrac{-i}{(2\pi)^{4}}\dfrac{\eta_{\mu\nu}}{q^{2}-i\epsilon}}\\\hphantom{XXXX}\times[\overline{u}_{3}(2\pi)^{4}ie\gamma^{\mu}\delta^{4}(p_{1}-q-p_{3})u_{1}]\end{array}\end{equation}$$\begin{equation}{\displaystyle \begin{array}{l}\int d^{\,4}q\left[\dfrac{\overline{u}_{4}}{(2\pi)^{3/2}}i(2\pi)^{4}e\gamma^{\nu}\delta^{4}(q+k_{2}-p_{4})\dfrac{\epsilon_{2\nu}}{(2\pi)^{3/2}\sqrt{2k_{2}^{0}}}\right]\dfrac{-i}{(2\pi)^{4}}\dfrac{-i\not q+m}{q^{2}+m^{2}-i\epsilon}\\\hphantom{XXXX}\times\left[\dfrac{\epsilon_{3\mu}^{*}}{(2\pi)^{3/2}\sqrt{2k_{3}^{0}}}i(2\pi)^{4}e\gamma^{\mu}\delta^{4}(p_{1}-q-k_{4})\dfrac{u_{1}}{(2\pi)^{3/2}}\right]\end{array}}\end{equation}$$\begin{equation}{\displaystyle \begin{aligned}\sum_{s_{\alpha},s_{\beta}}[\overline{u}_{\alpha}\Gamma u_{\beta}]^{*}[\overline{u}_{\alpha}\Gamma u_{\beta}] & =\sum_{s_{\beta}}\left[(\overline{u}_{\beta})^{i}\bigg(\left(\gamma^{0}\Gamma^{\dagger}\gamma^{0}\right)(\not\!p_{\alpha}+m)\Gamma\bigg)_{i}^{k}(u_{\beta})_{k}\right]\\& =\bigg(\left(\gamma^{0}\Gamma^{\dagger}\gamma^{0}\right)(\not\!p_{\alpha}+m)\Gamma\bigg)_{i}^{k}\left\{ \sum_{s_{\beta}}\left[(\overline{u}_{\beta})^{i}(u_{\beta})_{k}\right]\right\} \\& =\bigg(\left(\gamma^{0}\Gamma^{\dagger}\gamma^{0}\right)(\not\!p_{\alpha}+m)\Gamma\bigg)_{i}^{k}\left\{ \sum_{s_{\beta}}\left[(u_{\beta})_{k}(\overline{u}_{\beta})^{i}\right]\right\} \\& =\bigg(\left(\gamma^{0}\Gamma^{\dagger}\gamma^{0}\right)(\not\!p_{\alpha}+m)\Gamma\bigg)_{i}^{k}\left\{ (\not\!p_{\beta}+m)_{k}^{i}\right\} \\& =Tr\left[\left(\gamma^{0}\Gamma^{\dagger}\gamma^{0}\right)(\not\!p_{\alpha}+m)\Gamma(\not\!p_{\beta}+m)\right]\end{aligned}}\end{equation}$$\begin{equation}\begin{aligned}Tr\left[\gamma^{\alpha}\gamma^{\beta}\gamma^{\delta}\gamma^{\epsilon}\right] & =Tr\left[\left(2\eta^{\alpha\beta}-\gamma^{\beta}\gamma^{\alpha}\right)\gamma^{\delta}\gamma^{\epsilon}\right]\\& =2\eta^{\alpha\beta}Tr\left[\gamma^{\delta}\gamma^{\epsilon}\right]-Tr\left[\gamma^{\beta}\gamma^{\alpha}\gamma^{\delta}\gamma^{\epsilon}\right]\\
