Consider a multiway graph representing the time evolution of some quantum states.
Case 1: the edges merge (bosons)
I.e. the path weights add, and you get a single quantum state out of these multiple inputs
Case 2: the edges don’t merge (fermions)
If it is a pure tree, you have to go back to the beginning of the universe to get a merger: i.e. the states will be maximally separated in branchial space : i.e. they will have opposite phases And these states can never get together: i.e. the “electrons” can never wind up in the same state.
Essentially: the branchtime worldlines of different fermions do not converge, but they do for bosons.....
Total antisymmetry with n fermions: everything has to be at an opposite corner of branchial space
Minimal case: n independent paths.
Why exactly is it antisymmetrizing? I.e. are taking the various path weights, and combining