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From: Stefan Monnier <monnier@iro.umontreal.ca>
Newsgroups: gmane.emacs.help
Subject: Re: regexp problems the evil \[
Date: Thu, 23 Mar 2017 18:05:09 -0400
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>   (query-replace "\\[" "\\begin{displaymath}\n" nil)
     ^^^^^^^^^^^^^^^^^^^
     matches \[

>   (query-replace-regexp "\\[\\([^}]+\\)\\]" "@\\1" nil))
     ^^^^^^^^^^^^^^^^^^^^^^^^^
        matches [

Since [ in regexps has otherwise a special meaning.
To match \[ and \] you'll want

   (query-replace-regexp "\\\\\\[\\([^}]+\\)\\\\\\]" "@\\1" nil))


-- Stefan