It is forbidden to sit within four amos in any direction of someone davening Shemoneh Esrei. One reason for this is that the seated person would appear to lack interest in joining the person who is standing in prayer in accepting the yoke of Heaven. Additionally, since the area surrounding someone who is davening is imbued with holiness, sitting and pursuing mundane activities in that area demonstrates a denial of this holiness. It is permissible to sit in that area when one is involved in other aspects of tefilla such as the recitation of karbanos, though, since these are other forms of service of Hashem. Some hold that it is permissible to study Torah near someone davening, and this opinion may be relied upon in order to sit behind the davener or to sit in other areas around him when a special need arises. Thinking Torah thoughts without verbalizing them is not enough to permit one to sit near someone davening.

( סעיף א וס"ק ב, ה, ו ו־ז; ביאורים ומוספים דרשו, 7 ו־9)