Gemara

A case occurred in which R. Yirmeyah bar Aba was praying in back of Rav. Rav finished first. He did not interrupt R. Yirmeyah's Tefilah.

Inference: One may not pass in front of someone praying.

This supports R. Yehoshua ben Levi;

(R. Yehoshua ben Levi): One may not pass in front of someone praying.

Question: R. Ami and R. Asi pass in front of people praying!

Answer: They do not pass within four Amos.

Rishonim

Rambam (Hilchos Tefilah 5:6): One may not pass in front of someone standing in Tefilah, until he distances four Amos.

R. Yonah (18b DH Asur): One may not pass opposite someone praying, within four Amos. This is only in front. We are not concerned to pass to the side.

R. Yonah (DH Al): One may not pray in back of his Rebbi, lest his Rebbi will need to take three steps back while the Talmid is praying, and he cannot. If the Talmid distances four Amos, he may pray in back, for it looks like a separate Reshus.

Rashi (27a DH v'Lo): Rav did not interrupt between R. Yirmeyah and the wall, to pass in front of him and sit in his place. Rather, he remained standing in his place.

Poskim

Shulchan Aruch (OC 102:4): One may not pass opposite someone praying, within four Amos.

Mishnah Berurah (15): One may not pass, for it will distract the one praying. Therefore it is forbidden even if he (the one passing) is engaged in Keri'as Shema. The Chayei Adam says that it is because he interrupts between the one praying and the Shechinah.

Shulchan Aruch (ibid.): This is only in front. One may pass and stand to the side.

Magen Avraham (5): The Zohar forbids on every side.

Beis Yosef (DH u'Mutar): The Tur permits standing to the side. We learn from above (Sa'if 1), that the Isur is only to sit, but one may stand.

Rebuttal (Magen Avraham 6): If so, why does he say 'to the side'? One may stand even in front! I say that the Tur permits to pass to the side and stay there. One may not do so in front, for it will distract the one praying.

Prishah (1 DH v'Nir'eh): The Tur forbids passing opposite one praying within four Amos. If it is forbidden to sit in front, but one may stand in front, why is it forbidden to pass in front? It is unreasonable to say that passing is worse than standing. Also, we learn that one may pass to the side from a Kal va'Chomer from the Heter to stand to the side, like the Beis Yosef says. Rather, one may not sit in front for Malei Einav (as far as one can see), but within four Amos one may not even stand or pass. However, if so, why did the Tur mention in front, since it is unlike the sides? He did not mention in front of to teach about its Isur, rather, to teach about the Isur to the side. One might have asked 'what is the source that the verse comes to forbid the sides? Perhaps it forbids in front!' Therefore, the Tur taught about in front, i.e. there is a source to forbid in front, and to the side. Now that we know that within four Amos to the side is forbidden, also in back is forbidden, and in front Malei Einav. The Gematriya of 12 teaches about the sides and back.

Eliyahu Rabah (8): Olas Tamid asked what is the Chidush that one may stand to the side. One may stand even in front! Perhaps the Chidush is that one may go there l'Chatchilah and stand there. The only Heter in front is if he was already standing there, or if he was sitting he may stand, but l'Chatchilah one may not go to stand there, for he would need to stand in front of him a little. This is astounding. What is his source that one may stand in front? If it is because we forbid only sitting, and Eli stood, perhaps we forbid sitting in Malei Einav, but within four Amos even standing is forbidden! Rather, he must hold that the Tur forbids sitting [only] within four Amos. What was Olas Tamid's answer 'l'Chatchilah one may not go to stand there'? The Isur to sit is to sit now, but not if he was already sitting. If so, standing, which is permitted, is even to go to stand there! With difficulty, we could say that we exclude (i.e. permit) only if he was sitting and now stands. In any case this is like passing a little! Also, why didn't the Tur say that standing up in front is forbidden, like he wrote that it is permitted to the side? Also, he should have taught the Isur to stand up in front, rather than the Isur to pass in front, for the former is a greater Chidush! Rather, one may stand up in front. The Tur taught this regarding the sides, along with the Heter to pass there. Standing up does not show reluctance to accept Ol Malchus Shomayim. Maharil connotes like I said. What the Magen Avraham wrote is difficult.

Mishnah Berurah (16): The Magen Avraham holds that the sides in front of are (forbidden) like in front. The Eliyahu Rabah permits.

Mishnah Berurah (18): If the one praying can see the one passing, the sides in front are forbidden like in front, for this disturbs him. All the more so one may not go and stand in front, within four Amos. The Magen Avraham says so. Eliyahu Rabah forbids only passing into the four Amos in front of him, but (if one is already within four Amos) he may walk and stand, even in front of him. Perhaps one may be lenient in pressed circumstances.

Kaf ha'Chayim (21): Even if the one praying is in supplications after Shemoneh Esre, as long as he did not step back, one may not sit near of pass in front of him.

Bi'ur Halachah (DH Asur): Eliyahu Rabah brings from the Shlah that similarly, one should not pass when people are saying Shema Yisrael. Ma'amar Mordechai says that he disturbs the Kavanah of the one praying. If so, if he has a Talis over his face, it is permitted. We find that the Rema (128:3) says that Kohanim put the Talis over their hands so they will not look at their hands. A Kohen with Mumim may Duchan where this is the custom. In any case, it is proper to be stringent. Surely one must be stringent according to the Chayei Adam, who says that the Isur is because he interrupts between the one praying and the Shechinah.

Kaf ha'Chayim (22): Even if the one praying has a Talis over his face, it is forbidden. Chachamim did not distinguish. Also, he senses the footsteps, and this ruins his Kavanah. Also, the Zohar forbids due to a reason based on Kabalah. This is even if a Talis covers his head.

Mishnah Berurah (2): The Chayei Adam and Hilchos Ketanos say that if one prays on one side of something 10 Tefachim tall and four Tefachim wide, perhaps one may not pass on the other side, unless it is so tall that the one praying cannot see on the other side. Also the Eshel Avraham (90:38) forbids passing in an Almemra (an enclosure around the Bimah) opposite one praying, even though it is a separate Reshus, but one may sit in a separate Reshus, even within four Amos.

Kaf ha'Chayim (25): One may not pass in front of a Shali'ach Tzibur, even if he is praying something other than Shemoneh Esre.

Kaf ha'Chayim (27): The Magen Avraham did not mention that the Zohar forbids in front Malei Einav, for the Shulchan Aruch already mentioned this (in Sa'if 1, regarding the Isur to sit). One should be stringent like the Zohar when possible, also regarding to the sides and in back, unless it is pressed circumstances, e.g. he goes to pray or to a Mitzvah. Then, one may rely on the Mechaber.

Shulchan Aruch (5): If one finished his Tefilah and Ploni is praying in back of him, one may not take three steps back until Ploni finishes. If he steps back, this is like passing in front of one praying. One must be careful about this even if Ploni began praying after him, since Ploni already began.

Source: Mahari Avuhav, brought in Beis Yosef DH Kasav, learns this from the case of R. Yirmeyah.

Beis Yosef (ibid.): The Yerushalmi brings such a case in which R. Chiya bar Ba was praying, and Rav Kahana came and prayed in back of him. R. Chiya did not step back until Rav Kahana finished, even though Rav Kahana prayed at length.

Magen Avraham (7): Rashi connotes that one may step back, just he may not pass in front of one praying to return to his place. Perhaps Rashi holds that R. Yirmeyah was slightly far from Rav, so Rav could have taken three steps, so there is no proof from there. However, there is a proof from the Yerushalmi.

Machazik Berachah (4): R. Yonah forbids stepping into Ploni's four Amos. Rashi permits, just he may not pass in front of him. There is no proof from the Yerushalmi.

Mishnah Berurah (19): If he is not directly in back, rather, he is to the side, it seems that the Eliyahu Rabah permits.

Mishnah Berurah (20): The Shulchan Aruch discusses when he is within his four Amos, or will enter his four Amos through the three steps.