Optical Theorem: Understanding Conservation of Particles & Probability

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Discussion Overview

The discussion centers on the optical theorem and its implications regarding the conservation of particle number and probability, particularly in the context of elastic and inelastic scattering processes.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant suggests that the optical theorem is connected to conservation of particle number only in the case of elastic scattering, while inelastic processes do not conserve particle number.
  • Another participant argues that the optical theorem applies to inelastic scattering as well, indicating that the number of particles continuing forward is reduced by those that are scattered or absorbed, thus involving both elastic and inelastic cross sections.
  • A different participant questions whether particle number conservation holds in general, asserting that the applicability of the optical theorem to inelastic scattering implies that particles can be created or annihilated, leading to a lack of conservation.
  • A later reply affirms the previous participant's assertion regarding the absence of particle number conservation.

Areas of Agreement / Disagreement

Participants express disagreement regarding the conservation of particle number in the context of the optical theorem, with some asserting that it does not hold in inelastic scattering, while others maintain that the theorem encompasses both elastic and inelastic processes.

Contextual Notes

Participants highlight the dependence on the type of scattering process (elastic vs. inelastic) and the implications for particle number conservation, but do not resolve the nuances of these claims.

parton
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I'm confused. I read a line in a book where there was a qualitative explanation about the optical theorem, namely that it is connected with conservation of particle number. But I think that this is only true if we just consider elastic scattering. Inelastic processes would of course allow a change in the particle number so there is no conservation. The fundamental connection of the optical theorem is that with conservation of probability (because it follows from the unitarity of the S-matrix).

Is my "explanation" correct, or am I missing something?
 
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The theorem also applies for inelastic scattering.
It shows that the number of particles continuing forward is decreased by the number either scattered elastically or absorbed (or changed into something else).
That is why the total cross section (elasstic + inelastic) appears in the theorem.
 
my question is whether there's is particle number conservation in general? I would say no, because of the fact that the optical theorem also applies for inelastic scattering and there we could imagine processes where particles are created or annihilated. So there is no partcile number conservation.

Right?
 
Right.
 

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