1
$\begingroup$

We have virtual particles in quantum field theory (QFT). In general, they don't have the need to obey causality.

My question is:

Do the processes in QFT (electron self-energy, photon self-energy, electron-photon vertex, etc.) have to obey causality?
For example, can some parts of the electron self-energy diagram fall out of the light cone?
Or can some parts of the electron-positron annihilation process fall out of the light cone?

$\endgroup$
2
  • $\begingroup$ All the processes the can be measured obey causality. Virtual particles are simply not physical processes. They are mathematical terms in a perturbation series and one should treat them as such. The nomenclature is, to some extent, "unfortunate". If you go back to non-relativistic quantum mechanics and look at perturbation theory there, you will find that "virtual particles" are nothing special. In non-relativistic single quantum approximation they are summations/integrations over system states that are not actually eigenstates, if I remember correctly. $\endgroup$ Commented Jan 25 at 9:17
  • $\begingroup$ See this paper for the causality of the Dirac field: Phys. Rev. A 107, 032209 (2023) $\endgroup$
    – Quillo
    Commented May 15 at 23:08

1 Answer 1

0
$\begingroup$

No, to my knowledge causality is a crucial part of quantum field theory. Everything that can be measured has to obey causality. For bosons, this corresponds to the fact that $\langle 0|[\phi(x), \phi^*(y)]|0 \rangle$ is always zero at space-like separation. For fermions, we know that $\langle 0| \lbrace \psi(x), \bar{\psi}(y) \rbrace |0 \rangle$ is zero outside the light cone. Since operators such as charge, energy, and momentum always involve an even number of spinor fields, this is enough to ensure that $[\mathcal{O}_1(x), \mathcal{O}_2(y)]$ is also zero outside the light-cone. Which says no two measurements can effect each other at space-like separation.

By the way, I don't have a mathmatical proof of how the anticommutation relation is related to the commutator of the operators. I would love to see one.

$\endgroup$
2
  • $\begingroup$ physics.stackexchange.com/questions/159308/…: check this link virtual particles can violate causality and amplitude never dies off @tomtom1-4 $\endgroup$ Commented Oct 3, 2020 at 17:05
  • $\begingroup$ Amplitudes can be non-zero outside the light-cone. But two real measurements can not effect each other at space-like separation. So in a sense, you could argue that virtual particles can interact somewhat outside the light-cone but since you can not measure them it does not really matter. $\endgroup$
    – tomtom1-4
    Commented Oct 3, 2020 at 17:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.