Causality and the Role of Propagator in Quantum Field Theory

[wam_mi]

Hi All,

I am currently reading stuff about the propagator and causality in QFT at the moment and I don't really understand it. Could anyone explain this to me?

I understand that a propagator is a function which describes how particles and anti-particles travel from one place to another, but what is it to do with causality? Why is it important if the fields are space-like separated or time-like separated? What does it mean if the propagator does not give zero if it is outside the light-cone? How do we check if Causality is violated or not?

Thank you all!

 

[Bob_for_short]

Causality is provided with the commutators/anticommutators, not with propagators.

A photon propagator is just a Coulomb field slighly modified with relativistic and quantum corrections.

 

[wam_mi]

Causality is provided with the commutators/anticommutators, not with propagators.

A photon propagator is just a Coulomb field slighly modified with relativistic and quantum corrections.

Hi Bob_for_short,

Thank you for your reply.
Can I just ask you a couple of things please?

So you're saying, the commutators/anti-commutators determine causality?

(i) Is it true to say that if the two events are space-like separated, then the commutator vanishes under Lorentz transformation and so causality is preserved in this case?

(ii) What happens if the commutator does not vanish, in the case of time-like separated events or in the case of measurement outside the light cone? Do we have causality preserved?

Thank you for your help!
Kind regards

 

[Bob_for_short]

1) Yes,

2) No.

 

[wam_mi]

1) Yes,

2) No.

If causality is not preserved outside the light-cone, what does that mean?
How can we make sure the commutators would vanish?

 

[Bob_for_short]

We impose the value of commutator in the way that it vanishes outside the light cone. We impose it by hand. It is our requirement. Thus we ourselves construct a causal theory.