En passant is relatively insignificant in chess games and in orthodox chess problems. However, its action at a distance, its temporal dependency, and its general weirdness make it a very important element in retrograde analysis.
En passant (like castling) is a conditional move, whose legality in a position depends upon the history of the game. However, using retrograde analysis it may be possible to deduce whether or not the last move was the double step, and hence whether or not a given en passant capture is legal. This is based on the fundamental principle for chess problems, that any composition must show a legal position (i.e. one that can could appear during a game as the result of a sequence of legal moves).
Düna Zeitung, 1897
5+3. Mate in 2
By convention, with this kind of stipulation, we can assume that White has the move (unless the position is only legal with Black to play). Now by elimination, Black's last move can only have been 0 ... g7-g5. Note in particular that 0 ... Kg7-h6 is impossible since the White pawn on f6 could not have just moved to give check. Therefore, in the diagram position, en passant capture is legal. 1. h5xg6ep Kh5 2. Rxh7# solves the problem.
That was an example of proven e.p. legality. Here is one where there are two potential en passants, one of which is proved legal, and the other is proved illegal.
Thomas R. Dawson
Falkirk Herald 17/06/1914
11+6. Mate in 2
All missing Black pieces have been captured by White pawns. So Black's last move cannot have been 0 ... e7-e5 which would block the Black king's bishop from leaving its home square. By elimination, Black's last move must have been 0 ... c7-c5 and the queenside en passant is legal. The solution is hence 1. bxc6ep followed by 2. c7#.
This composition has appeared, upside down and with colours reversed, on chess problemists' Christmas cards!
The default convention is that, in a given position, if you can't deduce whether a potential en passant is legal or not, then it is not permitted. I.e., if uncertainly exists, you may assume that the last move was not the relevant double pawn move.
The en passant convention was initially designed for orthodox chess compositions, to remove what would otherwise be cooks. However, Retrograde Analysts have taken the convention and used it as a basis for many compositions, by deliberately exploiting situations where it's not possible to determine by logic whether or not a given en passant is legal. For example:
1467 Die Schwalbe 31 02/1975
dedicated to F. Schützhold
11+6. White retracts 1 move, then #1
If White retracts 1. Rg8xNh8 then Black's last move cannot be with the king because the prior check is impossible. This requires careful counting of pawn captures - specifically considering the history of the Black a pawn. The only other Black unit which might have moved is the b pawn, which cannot have come from c6 (again, by counting pawn captures). So the prior Black move was 0 ... b7-b5 and en passant is legal, hence 1. cxb6ep#. Check that if White retracts anything else, Black has at least one alternative last move, and by the en passant convention, en passant capture by White would not be allowed.
En passant capture is the only way to give a double check without moving either of the checking units. This makes it very interesting to use as the key retro-move to reach a position. It's easy to overlook this possibility when trying to solve a strange position. Of course, if you retract a5xb6ep (say) then the prior move can only have been b7-b5.
1st/2nd Prize 4th Thematic Tourney
6+1. Last 6 single moves?
White just gave check with his Ba1. This can only have been a discovered check but apparently no White piece could have been shielding the bK from the wB. Here an en passant capture explains the check: the wPe6 did it!
The last move was -1. d5xe6ep+ ! and the prior moves were -1 ... e7-e5 and -2. d4-d5+.
Now what was Black's move just before? It must have been played by the bK, running from a double check. The only possible move leading to an explainable double check involves another en passant capture. Black just played -2 ... Ke6xPf6!!, and the moves prior to that must have been -3. e5xf6ep+ f7-f5.
Note that again this problem uses the en passant rule heavily, but not the en passant convention. In fact, the convention isn't applicable to pure retrograde problems at all: it makes no statement to constrain the past of the game. All it says is that if the past is unclear, you are not permitted to play en passant going forwards.
This page has shown how a potential e.p. capture is handled in isolation. But retro analysts delight in the strange interactions possible with other conditional moves. For example, there are some situations where one of several en passant captures is legal but you can't tell which. And, there are situations where en passant interacts with castling in various ways. See the Castling and En-passant capture in the Codex 2009 and the spectacular A Posteriori convention.
Many thanks to Andrew Buchanan for providing this page!