Diagonal part of the configuration space of two indistinguishable quantum particles Why is the configuration space of two indistinguishable particles given by $\frac{M^n-\Delta}{S_n}$? My question is about the $\Delta$.
(Notation: $M$ is the configuration space of 1 particle. $M^n$ is the product space. $\Delta$ is the diagonal part : If $X=(x_i)_{1\leq i\leq n}\in M^n$, $X\in\Delta$ if $x_i=x_j$ for any two indices $i\neq j$. $S_n$ is the symmetry group on $n$ objects.)
I understand the mathematical convenience of removing $\Delta$, but what is the physical reasoning for saying that particles cannot sit on each other?
I looked at Laidlaw and DeWitt, they only say:

[...]Whether or not two point particles can simultaneously occupy the
  same point in space is not a question that we wish to settle here[...] 

Leinaas and Myrrheim removes $\Delta$ saying that these are singular. But real particles like bosons can in fact sit on top of each other.
 A: Some time ago I have asked a similar question; although I have accepted one of the answers, It did not satisfy my main interest concerning the physics of the case when the diagonal  $\Delta$ is not removed. 
Now I have some more information that I can share with you.
Most of the authors give two reasons for the removal of the diagonal:


*

*If we include the diagonal $\Delta$ , then the configuration space becomes an orbifold (The diagonal includes fixed points of the permutation group). (But, there is no conceptual problem in quantizing orbifolds).

*After the removal of the diagonal, the allowed quantizations for $d>2$ are only of bosonic and fermionic statistics in agreement with experiment ($d$ is the dimension of the single particle configuration space).

*Some authers also mention the impenetrability of the particles as a justification.


My new understanding is based on:


*

*In a recent work  N.P. Landsman shows for $d>2$ that although in the case when the diagonal is not removed, there are quantizations corresponding to parastatistics, However, (for $d>2$) all these quantizations can be reformulated as bosonic or fermionic quantizations with internal degrees of freedom.

*Landsman postpones his treatment of the cases $d=1,2$ for a future work, but there is an older work  by Bourdeau and Sorkin: (When can identical particles collide?) arguing that in the case $d = 2$ the discarding of the diagonal $\Delta$, removes legitimate quantization possibilities.
