how to put equation number at the bottom

Question

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?

Answer 1

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}

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}

Answer 2

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} 

Answer 3

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

\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.

Answer 4

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:

\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 ={} &.