Question about identical particles.

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Discussion Overview

The discussion centers around the indistinguishability of identical particles, specifically electrons, and the implications for scattering processes and S-Matrix calculations. Participants explore theoretical aspects of particle identity, wave packet separation, and the Pauli exclusion principle in the context of electron-electron scattering.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that two electrons with separated wave packets may be considered distinguishable, raising questions about the implications of this for scattering calculations.
  • Others argue that the principle of indistinguishability means that one cannot determine the specific locations of identical particles, even if they are far apart.
  • A participant inquires about the calculation of the S-Matrix for electron-electron scattering, noting the need to consider the Pauli exclusion principle.
  • Another participant provides a technical description of the scattering process, detailing the amplitudes for different scattering diagrams and the necessity of combining them with a relative minus sign due to antisymmetry.
  • There is a request for elaboration on the S-Matrix calculation, particularly in comparison to electron-muon scattering.

Areas of Agreement / Disagreement

Participants express differing views on the distinguishability of electrons based on their wave packet separation, and the discussion remains unresolved regarding the implications for scattering calculations and the S-Matrix.

Contextual Notes

Limitations include the lack of consensus on the interpretation of indistinguishability in various contexts and the specific mathematical steps involved in S-Matrix calculations for identical fermions.

ndung200790
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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?
 
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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.
 
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?
 
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')γμu(p1) (1/k2) u(p2')γμu(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')γμu(p1) (1/k2) u(p1')γμu(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.
 

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