# How does relativity lead to multi particles in Dirac and QFT, exactly

I have asked this question before on other forums, but only got the classical answer of the impossibility of the probability interpretation for single particle in QFT. Now, there seems to be also doubt in multi particle interpretation of the Dirac "sea". while in QFT the multi particle seems to be the result of promoting the wavefunction to an operator. And some people claimed it is a multi picture of a single particle. So, is there any clearer explanation?

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The Dirac equation has no bounded energy operator, so it does not qualify for a single-psrticle description without a restriction to the positive energy subspace. The latter restriction is ill-defined in case of a time-dependent external field, which implies that there is no fully consistent single-particle interpretation of the interacting Dirac equation.

In relativistic QFT, the need for cluster decomposition requires that the fields used are local, hence (for fermions) satisfy canonical anticommutation relations. The CAR for the free Dirac field leads to the need for antiparticles, hence for pair creation and annihilation, hence a multiparticle picture. This is spelled out in quite some detail in Volume I, Chapters 4 and 5 of Weinbergs book ''The QT of fields''.

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Thanks Arnold, I am familiar with the standard answer, But I was really asking, what IS IT about relativity that produces the multi particle picture. I will come back to your analysis a bit later. –  QSA Nov 15 '12 at 18:02
@QSA: it is 1. The need for positive energies, and 2. The need for cluster decomposition (which requires local fields). –  Arnold Neumaier Nov 16 '12 at 8:54

You can get non-relatavistic QFT's which are used to model condensed matter systems. It is not relativity that forces or allows QFT's to describe multi-particle states. QFT's are a natural formalism for multi-particle states as the Fourier modes of the field are quantized and so represent the number of particles with momentum corresponding to the Fourier wavelength. Relativity does however require the existence of anti-particles. One way to see this as those modes of the field that do not satisfy the energy momentum relation, $E^2=p^2+m^2$ would change the casual sequence of events depending on what frame they were viewed in,unless in some frames a particle can be viewed as an anti particle.

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Thanks.I alluded to the first paragraph in my OP. But I am not sure about the last sentence, can you please elaborate. –  QSA Nov 16 '12 at 2:15