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I'm using the class revtex4-1 to write a paper, and it has a very strange behaviour. Let me show you

enter image description here

In the above there is no problem, everything looks perfect. However, when I keep writing the following happen,

enter image description here

The problem!!!

The paragraph brakes and is written after the bibliography, and seems like a footnote.

More detailed data

  • The bibliography is generated by a couple of \footnotes
  • Equations (1) and (2) are part of an align environment
  • Since the equations are part of the previous paragraph, there is no intermediate line between the second \footnote and the align.
  • However, there is an empty line after the align.

What is wrong with this?

Surprisingly, if I leave an empty line after the second \footnote, the manuscript work as expected.

Am I doing something wrong? or Is it supposed to behave that way?

Sort of MWE

\documentclass[twocolumn,showpacs,showkeys,prd,superscriptaddress]{revtex4-1}

\usepackage{amsmath,amssymb,amsfonts,dsfont,mathrsfs,amsthm}
\usepackage{graphicx}
\usepackage{centernot}
\usepackage{hyperref}
\usepackage{xcolor}
\usepackage{comment}
\hypersetup{linktocpage,colorlinks=true,urlcolor=blue!80!red,linkcolor=blue,citecolor=red}
\usepackage{feynmf}
\usepackage{siunitx}
\usepackage{array}
\usepackage{ulem}
\usepackage{tikz}
\usepackage{braket}

%%% Lots of command definitions

\newcommand{\cdf}{{\boldsymbol{\mathcal{D}}}}
\newcommand{\df}[1][]{\,{\mathbf{d}}{#1}\!}
\newcommand{\Tf}[1]{\,\boldsymbol{\mathcal{T}}^{#1}}
\newcommand{\w}{{\scriptstyle\wedge}}
\newcommand\vi[2]{e^{{#1}}_{{#2}}}
\newcommand\vif[1]{\,{\mathbf{e}}^{{#1}}}
\newcommand\spi[1]{\omega_{{#1}}}
\newcommand\tspi[1]{\tilde{\omega}_{{#1}}}
\newcommand\spif[2]{\,{\boldsymbol{\omega}}^{{#1}}{}_{{#2}}}
\newcommand\tspif[2]{\,{\tilde{\boldsymbol{\omega}}}^{{#1}}{}_{{#2}}}
\newcommand{\Rif}[2]{\,\boldsymbol{\mathcal{R}}^{{#1}}{}_{{#2}}}
\newcommand{\tRif}[2]{\,\tilde{\boldsymbol{\mathcal{R}}}^{{#1}}{}_{{#2}}}
\newcommand*{\diag}{\operatorname{diag}}
\newcommand{\contf}[2]{\,\boldsymbol{\mathcal{K}}^{#1}{}_{#2}}

\begin{document}

\title{Strong CP Conservation through Spacetime with Torsion}

\author{Oscar \surname{Castillo-Felisola}}
%\email{o.castillo.felisola@gmail.com} 
\affiliation{Departamento de F\'isica, Universidad T\'ecnica Federico Santa Mar\'ia, \\Casilla 110-V, Valpara\'iso, Chile.}
\affiliation{Centro Cient\'ifico Tecnol\'ogico de Valpara\'iso, Valpara\'iso, Chile.}

\author{Crist\'obal \surname{Corral}}
\email{cristobal.corral@postgrado.usm.cl}
\affiliation{Departamento de F\'isica, Universidad T\'ecnica Federico Santa Mar\'ia, \\Casilla 110-V, Valpara\'iso, Chile.}

\author{Sergey \surname{Kovalenko}}
%\email{sergey.kovalenko@usm.cl}  
\affiliation{Departamento de F\'isica, Universidad T\'ecnica Federico Santa Mar\'ia, \\Casilla 110-V, Valpara\'iso, Chile.}
\affiliation{Centro Cient\'ifico Tecnol\'ogico de Valpara\'iso, Valpara\'iso, Chile.}

\author{Valery E. \surname{Lyubovitskij}}
%\email{valeri.lyubovitskij@uni-tuebingen.de}  
\affiliation{Institut f\"ur Theoretische Physik, Universit\"at T\"ubingen, \\ Kepler Center for Astro and Particle Physics, \\ Auf der Morgenstelle 14, D-72076 T\"ubingen, Germany}

\author{Iv\'an \surname{Schmidt}}
%\email{sergey.kovalenko@usm.cl}  
\affiliation{Departamento de F\'isica, Universidad T\'ecnica Federico Santa Mar\'ia, \\Casilla 110-V, Valpara\'iso, Chile.}
\affiliation{Centro Cient\'ifico Tecnol\'ogico de Valpara\'iso, Valpara\'iso, Chile.}

\begin{abstract}
  Bla..Bla..Bla..
\end{abstract}

\maketitle

In this paper we present arguments which allow to realize a Peccei-Quinn-like solution to  the strong CP problem in a gravitational fashion, by allowing nonvanishing torsion in the gravitational sector. The existence of torsion permeates to the fermionic sector through the covariant derivative, while the gauge and scalar sectors are innocuous to the generalization.

In the standard construction of Einstein-Hilbert theory~(EHT) of gravity, \textit{aka} General Relativity, it is assumed that the connection is compatible with the metric (metricity condition), \mbox{$\nabla g = 0$}, and additionally the Christoffel symbols are chosen to be the Levi-Civita connection, which is completely determined by the metric. However, since the early 20's it has been known that the last condition is not necessary, and the gravitational theory can be generalized slightly by allowing a nonvanishing torsion. %~\cite{Cartan1923,Cartan1924,Cartan1925,}.

Cartan's generalization of gravity, or Einstein-Cartan theory (ECT), was not considered seriously until attempts of coupling fermionic matter to gravity were taken into account. Great advances in this respect were obtained by analyzing possible ``Theories of Everything'', such as string theory, during the 60's and 70's.

Although the standard formalism for studying  gravitational theories, involving the metric and their derivatives, is known as second order formalism, an alternative procedure known as first order formalism can be constructed by considering two independent fields, called vielbein ($\vi{a}{\mu}$) and spin connection ($\spi{\mu}{}^{ab}$)~\footnote{The vielbein is related to the metric through the the identity \mbox{$g_{\mu\nu} = \eta_{ab} \vi{a}{\mu} \vi{b}{\nu}$,} with \mbox{$\eta =\diag(-1,1,1,1)$.} Also, $\spi{\mu}$ is a connection with respect to the Lorentz group of the tangent space.}.

Either way, the exterior calculus develop by Cartan is a natural playground for these theories. In general, Riemann-Cartan manifolds are characterized by their curvature and torsion, which are related with the vielbein and spin connection via the structural equations,~\footnote{Through the paper the bold symbols represent differential forms. Moreover, coordinated and non-coordinated basis are used indifferently, \textit{i.e.}, \mbox{$\Rif{ab}{\mu\nu}\df[x^\mu]\w\df[x^\nu] = \Rif{ab}{cd}\vif{c}\w\vif{d}$.}} %%% After leaving am empty line here the problem solves
\begin{align}
  \df\vif{a} + \spif{a}{b}\w\vif{b} &= \Tf{a} \label{first-str-eq}, \\
  %% \intertext{and}
  \df\spif{a}{c} + \spif{a}{b}\w\spif{b}{c} &= \Rif{a}{c}. \label{sec-str-eq}
\end{align}

Notice that the spin connection can be split into $\spif{ab}{} = \tspif{ab}{} + \contf{ab}{}$, where the tilde indicates torsion-free and the contorsion tensor encodes the information about the torsion, $\Tf{a} = \contf{a}{b}\w\vif{b}$. Similarly, Eq.~\eqref{sec-str-eq} yields
\begin{align}
  \Rif{ac}{} = \tRif{ac}{} + \tilde{\cdf}\contf{ac}{} + \contf{a}{b}\w\contf{b}{c}
\end{align}

\bibliographystyle{apsrev4-1}
\bibliography{References}
  • Why not make the code compilable? – mvkorpel Jul 9 '14 at 12:24
  • @mvkorpel Let me try! – Dox Jul 9 '14 at 12:29
  • 1
    The problem seems to lie in the single line align at the end, which is incorrect anyway: a single line display should use equation. – egreg Jul 9 '14 at 13:21
  • @egreg You're right! (as usual)... Might I ask, Why does it make such a difference? – Dox Jul 9 '14 at 13:25
  • 1
    @Dox I'm not really sure, but when I saw the one line align I immediately changed it to equation. It might be a bug in revtex anyway. If I use the same two line align as the preceding one instead of the last equation, the page break is correct. – egreg Jul 9 '14 at 13:31
3

It's not clear what the real reason is; however, changing the last align into equation seems to solve the issue.

Apparently, the one line align confuses somewhat revtex4-1. In any case, using align for single line equations is not recommended.

I made an experiment using a two row align in the last environment and the page break is good. So it really seems a problem with the single row align.

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