'Off-shell' particle in an external field....

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Discussion Overview

The discussion revolves around the concept of 'off-shell' particles in the context of external fields, exploring the implications of this terminology for real, observable particles. Participants seek clarification on the meaning and significance of being 'off-shell' when energy conservation is still applicable.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions why a real, 'observable' particle is considered 'off-shell' in an external field, referencing A. Neumaier's FAQ notes about the mass shell constraints losing meaning in this scenario.
  • Another participant suggests that 'off-shell' may indicate that the external field influences the energy of the particle.
  • A further contribution reiterates the definition of 'off-shell' as a condition where the standard relation $p^2=m^2$ is not satisfied, which defines the on-shell condition.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the implications of 'off-shell' terminology, and there is no clear consensus on the interpretation of this concept in the context of external fields.

Contextual Notes

The discussion highlights the dependence on definitions related to 'on-shell' and 'off-shell' conditions, as well as the implications of external fields on particle behavior, which remain unresolved.

asimov42
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Questioning why particles are said to be 'off-shell' in an external field...
Silly question but could someone explain why a real, 'observable' particle is said to be 'off-shell' in an external field? @A. Neumaier 's excellent FAQ notes that the mass shell constraints ceases to have meaning in this case. I'm just not fully clear on why (probably obvious) given that energy conservation still holds.
 
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Or is the use of 'off shell' in this case simply to indicate that the field may influence the energy of the particle?
 
asimov42 said:
could someone explain why a real, 'observable' particle is said to be 'off-shell' in an external field?
asimov42 said:
Or is the use of 'off shell' in this case simply to indicate that the field may influence the energy of the particle?
Off shell just means that the standard asymptotic (or free field) relation $p^2=m^2$ (in units where $c=1$), which defines the on shell condition, is not satisfied.
 

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