Halacha requires that preferably a man wear a covering on his head at all times. Does this requirement apply only when a person is in motion, or even when he is stationary when he stands or sits in one place?
The Magen Avraham (commentary to the Shulchan Aruch by Rabbi Avraham Gombiner, Poland, 1637-1683) in Orach Hayim Siman 282, Seif Kattan 8, claims that one need not keep his head covered while stationary, and he draws proof to this ruling from the Gemara in Masechet Yoma. The Gemara describes the procedure for the "Payis" the lottery conducted in the Temple each day to determine which Kohanim would perform the various rituals. The person conducting the lottery would remove the Mitznefet (hat) from the head of one of the Kohanim and begin the lottery with that Kohen. It thus emerges from the Gemara that one of the Kohanim stood bareheaded during this procedure, indicating that while standing in one place one need not cover his head.
This is the ruling of several other authorities, as well, including the Beit Meir (work of Halacha by Rabbi Meir Posner, Poland, 18th century siman 2) and the Leket Yosher (biography and rulings of Rabbi Yisrael Isserlin, Germany-Austria, 1390-1460 vol. 1, p. 31).
By contrast, the Peri Megadim (Rabbi Yosef Te'omim, Poland-Germany, 1727-1792), in Eishel Avraham (2:6), as well as the Sedei Chemed (work by Rabbi Chayim Chizkiya Halevi, Turkey-Israel, 1832-1904 Kelal 71), disagree, and require wearing a head-covering even while stationary. They argue that the Kohen whose Mitznefet was removed very likely wore another, smaller head-covering underneath, and one therefore cannot prove from this Gemara that the Kohen was allowed to stand bareheaded.
It should be noted that even according to the lenient position, one must wear a head-covering while sitting or standing in a synagogue. The Tosfot tells that the "Payis" would not take place in the Azara, the courtyard of the Temple, and it is explained that it would be inappropriate for a Kohen to stand bareheaded within the sacred grounds of the Beit Ha'mikdash. Thus, even if it is permissible to stand or sit without a head-covering generally, in holy places, such as a synagogue, this would be forbidden.
Summary: There is some disagreement among the authorities as to whether one must wear a head-covering while he is sitting or standing in one place. In a synagogue, however, all authorities agree that one must wear a head-covering at all times, even while staying in one place.
