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.