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It's because first homotopy group for configuration space of one-particle states in 3D space is permutations group. In two words: scalar product $\langle \mathbf p_{1}, \mathbf p_{2}, ...| \mathbf k_{1}, \mathbf k_{2} , ...\rangle$ is invariant under simultaneous permutations $\mathbf p$ and $\mathbf k$ for different particles. For identical particles, ...


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Sometimes when people try to simplify physics they go too far and oversimplify. An example would be if people tell you that two atoms of $He^4$ can be in the same state because they "are bosons." First let's look at one fermion, say an electron. It has a spin and a spatial extent, the general state of the electron is a product of the spin and the spatial ...



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