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

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In an external field, a real, observable particle is considered 'off-shell' because it does not satisfy the standard mass shell condition, where the energy-momentum relation p^2=m^2 holds. This deviation indicates that the particle's energy can be influenced by the external field, leading to changes in its effective mass. The term 'off-shell' highlights that the usual constraints of energy conservation still apply, but the particle's properties are altered by the field. Understanding this concept is essential in quantum field theory, as it reflects the interaction between particles and external influences. The discussion clarifies the implications of being 'off-shell' in the context of observable particles.
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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