我正在用这个类revtex4-1写一篇论文，它的行为非常奇怪。让我给你演示一下
上面没有任何问题，一切看起来都很完美。然而，当我继续写的时候，发生了以下事情，
问题！！！
本段中断于参考书目之后，类似脚注。
更详细的数据
- 书目由几个
\footnotes生成 - 方程（1）和（2）是
align环境的一部分 \footnote由于方程式是上一段的一部分，因此第二段和之间没有中间线align。- 但是，后面有一个空行
align。
这有什么问题？
令人惊讶的是，如果我在第二个之后留一个空行\footnote，手稿就会按预期工作。
难道我做错了什么？或者它应该表现得那样吗？
属于 MWE 类型
\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{[email protected]}
\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{[email protected]}
\affiliation{Departamento de F\'isica, Universidad T\'ecnica Federico Santa Mar\'ia, \\Casilla 110-V, Valpara\'iso, Chile.}
\author{Sergey \surname{Kovalenko}}
%\email{[email protected]}
\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{[email protected]}
\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{[email protected]}
\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}
答案1
目前尚不清楚真正的原因是什么；但是，将最后一个改为align似乎equation可以解决问题。
显然，一行align有点令人困惑revtex4-1。无论如何，align不建议使用单行方程。
我在上一个环境中使用两行进行了实验align，分页效果很好。因此，单行似乎确实存在问题align。