4

i want my eq number 11.72 to appear at the last line.how can i do that?

After a wick rotation we obtain


\begin{equation}
\begin{split}
\int \frac{d^4 \mathnormal{k}}{(2\pi)^4}\text{log}(-k^2+m^2)=& i\int 
  \frac{d^4 \mathnormal{k_E}}{(2\pi)^4}\text{log}(k_E^2+m^2)\\
  =&-i \frac{\partial}{\partial \alpha}\int \frac{d^4 
    \mathnormal{k_E}}{(2\pi)^4}\frac{1} 
    {(k_E^2+m^2)^{\alpha}}\Big\vert_{\alpha=0}\\
  =&-i \frac{\partial}{\partial \alpha} \Big(\frac{1} 
     {(4\pi)^{d/2}}\frac{\Gamma(\alpha-\frac{d}{2})} 
   {\Gamma(\alpha)}\frac{1}{(m^2)^{\alpha-\frac{d}{2}}} \Big) \Big 
    \vert_{\alpha=0}\\
       =& -i\frac{\Gamma(\frac{-d}{2})}{(4\pi)^{d/2}}\frac{1}{(m^2)^{- 
        d/2}}
       \end{split}
      \tag{11.72}
      \end{equation}

this is the pdf i obtain.how can i put the eq. number at the bottom? enter image description here

2

Like this.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
\int \frac{d^4 \mathnormal{k}}{(2\pi)^4}\text{log}(-k^2+m^2)=& i\int 
  \frac{d^4 \mathnormal{k_E}}{(2\pi)^4}\text{log}(k_E^2+m^2)\notag\\
  =&-i \frac{\partial}{\partial \alpha}\int \frac{d^4 
    \mathnormal{k_E}}{(2\pi)^4}\frac{1} 
    {(k_E^2+m^2)^{\alpha}}\Big\vert_{\alpha=0}\notag\\
  =&-i \frac{\partial}{\partial \alpha} \Big(\frac{1} 
     {(4\pi)^{d/2}}\frac{\Gamma(\alpha-\frac{d}{2})} 
   {\Gamma(\alpha)}\frac{1}{(m^2)^{\alpha-\frac{d}{2}}} \Big) \Big 
    \vert_{\alpha=0}\notag\\
       =& -i\frac{\Gamma(\frac{-d}{2})}{(4\pi)^{d/2}}\frac{1}{(m^2)^{- 
        d/2}}
      \tag{11.72}
      \end{align}
\end{document}

enter image description here

However, I would at least use \log instead of \text{log} and make the differential d distiguishable from the dimension d in dimensional regularization, and same for the imaginary i. Nor would I set the equation number by hand.

\documentclass{article}
\usepackage{amsmath}
\usepackage{cleveref}
\newcommand{\dd}[1]{\mathrm{d}#1}
\numberwithin{equation}{section}
\begin{document}
\section{Dimensional regularization}

\dots

After a Wick rotation we get
\begin{align}
\int\! \frac{\dd^4 \mathnormal{k}}{(2\pi)^4}\log(-k^2+m^2)&= \mathrm{i}\,\int\! 
  \frac{\dd^4 \mathnormal{k_E}}{(2\pi)^4}\log(k_E^2+m^2)\notag\\
  &=-\mathrm{i} \frac{\partial}{\partial \alpha}\int\! \frac{\dd^4 
    \mathnormal{k_E}}{(2\pi)^4}\frac{1} 
    {(k_E^2+m^2)^{\alpha}}\Big\vert_{\alpha=0}\notag\\
  &=-\mathrm{i}\, \frac{\partial}{\partial \alpha} \Big(\frac{1} 
     {(4\pi)^{d/2}}\frac{\Gamma(\alpha-\frac{d}{2})} 
   {\Gamma(\alpha)}\frac{1}{(m^2)^{\alpha-\frac{d}{2}}} \Big) \Big 
    \vert_{\alpha=0}\notag\\
       &= -\mathrm{i}\,\frac{\Gamma(\frac{-d}{2})}{(4\pi)^{d/2}}
       \frac{1}{(m^2)^{- 
        d/2}}
 \label{eq:DimRegInt1}
\end{align}

\dots

As shown in \cref{eq:DimRegInt1}, \dots

\end{document}

enter image description here

3
  • thank you sir.i dont understand what u asked? everytime i write \tag{eq.nmbr} in the equation environment.is there a better way?are u sugesting to make a user tag shortcut? Nov 29 '18 at 4:10
  • ok i will use different d's.thanks for the suggestion. Nov 29 '18 at 4:11
  • @jowadulkader Of course there is a better way. If you just remove the \tag from the last line, the equation will have an automatic number, and you could label the equation, e.g. \label{eq:DimRegIntegral1}, and then refer to it with \eqref{eq:DimRegIntegral1} at some other point. If you want the section number in the equation, use \numberwithin{equation}{section}. I changed my example accordingly.
    – user121799
    Nov 29 '18 at 4:15
1

You can simply replace split with aligned and use the [b] optional argument.

I took the liberty to change the size of the big delimiters to \bigg, which look better in this context, in my opinion.

\documentclass{article}
\usepackage{amsmath} 

\begin{document} 

\begin{equation}
    \begin{aligned}[b]
    \int \frac{d^4 \mathnormal{k}}{(2\pi)^4}\text{log}(-k^2+m^2)&= i\int
    \frac{d^4 \mathnormal{k_E}}{(2\pi)^4}\text{log}(k_E^2+m^2)\\
    &=-i \frac{\partial}{\partial \alpha}\int \frac{d^4
    \mathnormal{k_E}}{(2\pi)^4}\frac{1}
    {(k_E^2+m^2)^{\alpha}}\bigg\vert_{\alpha=0}\\
    &=-i \frac{\partial}{\partial \alpha} \biggl(\frac{1}
     {(4\pi)^{d/2}}\frac{\Gamma(\alpha-\frac{d}{2})}
   {\Gamma(\alpha)}\frac{1}{(m^2)^{\alpha-\frac{d}{2}}} \biggr) \bigg
    \vert_{\alpha=0}\\
      & = -i\frac{\Gamma(\frac{-d}{2})}{(4\pi)^{d/2}}\frac{1}{(m^2)^{-
        d/2}}
    \end{aligned}
  \tag{11.72}
\end{equation}. 

\end{document} 

enter image description here

0

The following cleans things up a bit, including using a combination of \nonumber (or \notag) to remove equation numbers where necessary and specify a hard-coded equation number with \tag:

enter image description here

\documentclass{article}

\usepackage{amsmath,mleftright}

\begin{document}

\begin{align}
  \int \frac{\mathrm{d}^4 k}{(2 \pi)^4} \log \bigl(-k^2 + m^2 \bigr)
    &=  i \int \frac{\mathrm{d}^4 k_E}{(2 \pi)^4} \log \bigl(k_E^2 + m^2 \bigr) \nonumber \\
    &= -i \mleft. \frac{\partial}{\partial \alpha} \int \frac{\mathrm{d}^4 k_E}{(2 \pi)^4}
      \frac{1}{\bigl(k_E^2 + m^2 \bigr)^\alpha} \mright\rvert_{\alpha = 0} \nonumber      \\
    &= -i \mleft. \frac{\partial}{\partial \alpha} \biggl(
      \frac{1}{(4 \pi)^{d / 2}} \frac{\Gamma(\alpha - d/2)}{\Gamma(\alpha)} 
      \frac{1}{(m^2)^{\alpha - d/2}} \biggr) \mright\rvert_{\alpha = 0} \nonumber         \\
    &= -i \frac{\Gamma(-d / 2)}{(4 \pi)^{d / 2}} \frac{1}{(m^2)^{-d / 2}} \tag{11.72}
\end{align}

\end{document}

Some pointers:

  • It seems unnecessary to use \frac in an exponent/superscript (or subscript for that matter) if it's just single tokens. That is, a/b seems cleaner than \frac{a}{b}.

  • Use the (operator) \log instead of \text{log}.

  • Stretch extensible delimiters (like \rvert above) using a combination of \mleft...\mright (thanks to mleftright, alternatively use \left...\right, but the spacing might be mildly different/wider).

  • align alignment around = should use &=, not =&. You can use the latter, but then you need ={} &.

4
  • @marmot: I saw your answer and it was lacking, so I wrote my own. Why do you think that "I took your answer"?
    – Werner
    Nov 29 '18 at 4:25
  • @marmot: Yes. And what does that have to do with this?
    – Werner
    Nov 29 '18 at 4:29
  • @marmot: You've got it completely wrong. The linked post about potrace does not imply that I want credit for something I wrote years before. It provide a link in the right-hand margin of the post thread that identifies linked posts. That way someone who finds the one could potentially be interested in the linked question; roughly a way to identify related posts. Secondly, align is a generic way of aligning equations around some alignment point; there's nothing special about it, nor does your "first use" in some answer void anyone else's use of that in a future answer...
    – Werner
    Nov 29 '18 at 4:36
  • 1
    @marmot: ...the Internet can be a mean place, and there's not need to try and own a space that is free for anyone to contribute. This is not about you, but about the person who asks the question and how contributions add to the community. I did not want to point out all the possible changes that I would implement in your answer, since it wouldn't add value. I just wrote up something that I thought would be more clean and also accurate in terms of the spacing correction originally posted.
    – Werner
    Nov 29 '18 at 4:37
0

There is an option tbtags to the amsmath package that does this for you:

Sample output

\documentclass{article}

\usepackage[tbtags]{amsmath}

\begin{document}

\begin{equation}
  \begin{split}
    \int \frac{d^4 k}{(2\pi)^4}\log(-k^2+m^2)
    &= i\int \frac{d^4 k_E}{(2\pi)^4}\log(k_E^2+m^2)\\
    &=-i \frac{\partial}{\partial \alpha}\int \frac{d^4
       k_E}{(2\pi)^4}\frac{1}
       {(k_E^2+m^2)^{\alpha}}\Bigr\vert_{\alpha=0}\\
    &=-i \frac{\partial}{\partial \alpha} \Bigl(\frac{1}
       {(4\pi)^{d/2}}\frac{\Gamma(\alpha-\frac{d}{2})}
       {\Gamma(\alpha)}\frac{1}{(m^2)^{\alpha-\frac{d}{2}}} \Bigr) \Bigr
       \vert_{\alpha=0}\\
    &= -i\frac{\Gamma(\frac{-d}{2})}{(4\pi)^{d/2}}\frac{1}{(m^2)^{-
       d/2}}
  \end{split}
  \tag{11.72}
\end{equation}

\end{document}

Other changes

  • =& to &= (if you really want to align after = then you need to write ={}& for correct spacing)
  • \Big to \Bigl or \Bigr for correct spacing
  • \text{log} to \log
  • \mathnormal removed, was not used consistently and had no effect

The opposite of the tbtags option is the default centertags. The name tbtags derives from "top or bottom tags"; it will place tags at the top if equation numbers are on the left, or at the bottom if equation numbers are on the right.

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