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In Coleman's lecture on quantum field theory he says that when a particle is confined in in a region shorter than its Compton wavelength, very many particles can be produced. My question is whether this will happen even in vacuum and, if so, where does the energy required for their production come from?

People explain these using uncertainty principle in the form of the energy-time uncertainty relation. However, in quantum field theory, the only uncertainty principle is the uncertainty between a field $\phi(x)$ and the conjugate momentum $\pi(x)$.

EDIT: Page 16 of this note by Coleman.

SRS
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    Please link to the lecture in question. – Emilio Pisanty Nov 12 '16 at 20:32
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    I am not sure what you mean. In vacuum there is no particle to confine in the first place. – Prof. Legolasov Nov 13 '16 at 02:40
  • @SolenodonParadoxus I think, he's talking about one real quanta confined between two plates in an evacuated environment. – SRS Mar 08 '17 at 19:13
  • Hi. I don' t know if one can interpret the $\Delta \phi$ or $\Delta \pi$ in the uncertainty relation $\Delta \phi \Delta \pi >= 0$ as quantum fluctuations if the fields. See maybe http://physics.stackexchange.com/questions/191042/uncertainty-principle-in-quantum-field-theory – Constantine Black Mar 15 '17 at 17:40

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Yes, this will happen. But you cannot confine particle in the vacuum. To confine a particle, you must have some potential. The energy to produce pairs must come exactly from this binding potential. For example, you can confine electron using a very strong electric field. To confine an electron in a region smaller than its Compton wavelength you need a field with enough energy to create electron position pairs. Particle in a vacuum will never be confined.

Veritas
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  • If particles in a vacuum can never be confined without an external potential, then what about the case of quark confinement? Thanks – Davius Aug 26 '23 at 19:04