If you're not using any form of automatic capitalization in your document, add
\let\MakeUppercase\relax
to your document preamble. This makes \MakeUppercase (used in the default book document class to make the capitalize the headers) turn into a no-op.

However, other elements of your document might still use this without you knowing it. It's better to define these headers in an abstract and manageable way through page styles. Here's one using titleps:
\usepackage{titleps}% http://ctan.org/pkg/titleps
\makeatletter
\newpagestyle{main}{% Define page style main
\sethead%
[\slshape\thesection.\ \sectiontitle][][]% [<even-left>][<even-centre>][<even-right>]
{}{}{\slshape\@chapapp~\thechapter.\ \chaptertitle}% {<odd-left>}{<odd-centre>}{<odd-right>}
\setfoot{}{\thepage}{}% {<left>}{<centre>}{<right>}
}
\pagestyle{main}% Use page style main
Some more details are available from the titleps documentation or from titleps for fancyhdr users.
Chapter 1. Chapter one $e^--p^+$and notCHAPTER 1. CHAPTER ONE $E^--P^+$? Or justCHAPTER 1. CHAPTER ONE $e^--p^+$? – Werner Jun 28 '13 at 15:44\let\MakeUppercase\relaxto your document preamble. – Werner Jun 28 '13 at 15:53\uppercasenonmaththat was written for this purpose. you might be able to extract it (and some other required definitions) fromamsbook.cls. the macro documentation is inamsclass.dtx, which can be found on ctan in themacros/latex/required/amslatex/amscls/area; a somewhat more "readable" version (a pdf file generated from the.dtx) can be had withtexdoc amsclass' on a tex live installation (if the documentation has been installed), or from ctan in thedoc` subdirectory of the cited area. – barbara beeton Jun 28 '13 at 18:51