Question about identical particles.

[ndung200790]

The undistinguishable principle of identical particles says we can not distinguish the identical particles.But I think that two electrons(for example) having the wave packets that are separated with each other are distinguishable(?).

Can we distinguish two particles that their wave packets overlaped if before their wave packets being overlaped they stay in two determine different states?

In so far I have not seen any book considers the scattering of two electrons(meaning two identical fermions).How can we calculate the S-Matrix,because in this case we have to also consider the effect of exclusive principle of Pauli?

 

[Bill_K]

The undistinguishable principle of identical particles says we can not distinguish the identical particles.But I think that two electrons(for example) having the wave packets that are separated with each other are distinguishable(?).

If you have one electron on Earth and one electron on Mars, "indistinguishable" means you cannot tell whether electron #1 is on Earth and #2 is on Mars, or the other way around.

In so far I have not seen any book considers the scattering of two electrons(meaning two identical fermions).How can we calculate the S-Matrix,because in this case we have to also consider the effect of exclusive principle of Pauli?

The two particles can only be in an antisymmetric state. If both are spin up, say, then L must be odd. Or if their spins are in a singlet state, then L must be even.

 

[ndung200790]

Could you give me a more elaboration about the calculation of the S-Matrix.In electron-muon scattering, they use the tree diagram of Feynman(at lowest order),but what about the electron-electron scattering?

 

[Bill_K]

For electron-electron scattering, a pair of electrons with momenta p₁, p₂ scatter to a pair with momenta p₁', p₂'. The amplitude is something like

u(p₁')γ^μu(p₁) (1/k²) u(p₂')γ^μu(p₂)

But since the electrons are indistinguishable, they may also scatter to momenta p₂', p₁'. This is a second diagram. The amplitude for this diagram is

u(p₂')γ^μu(p₁) (1/k²) u(p₁')γ^μu(p₂)

The two amplitudes must be combined, with a relative minus sign to take care of the antisymmetry.

For electron-muon scattering you would have just one diagram.