Is there a description of collapse in QFT ?

[dreynaud]

In QM we have the postulate of measure giving rise to the notion of wave function collapse through measurement.

Is there an analog description of collapse in QFT (even an effective one) ? And what is then collapsing ? The field ? What would that mean ?

I'm interested for references on the subject.

 

[Fredrik]

The postulate you're talking about applies to all quantum mechanical theories, including quantum field theories. A "collapse" is a projection of the state vector onto an eigenstate. The only mechanism I have heard of that offers some sort of explanation is decoherence. The idea is that interactions with the environment select a particular basis of the Hilbert space and make the density operator almost diagonal in that basis. Note that this isn't really a collapse. A collapse would be represented by a density matrix that's exactly diagonal.

 

[dreynaud]

Yes I know some things about decoherence.
In the idealized case where density matrix is diagonal (after infinite time in the decoherence theory if I'm not wrong), the out state could then be written in term of field operators acting on the vaccum. So can we say that the field is collapsing ? That seems a reasonable QFT counterpart of the QM postulate no ?
(Note I agree that decoherence brings a much more detailed description than hte idealized situation I consider).

Another particular point I had in head is the relativistic invariance which is a caracteristic of QFT compared to QM.
QM collapse simultaneously cancels the wave function for all eigenstates different than the effectively observed one. What about this in the context of QFT ?
For example, in the simple case of a field with one particle, one detects it at some position in the space.
Does the "collapse" occurs simultaneously ? in which reference frame ? how can it be consistent with change of reference frame ?
Or the "collapse" occurs everywhere outside the light-cone ?
Other ?
What says the decoherence about that ?

 

[Demystifier]

1. QFT has nothing new to say about the "mystery" called collapse.
2. The object that collapses in QFT is not the field, but the quantum state, i.e., a vector in the representation space of the field operator.
3. I think it is misleading to think about the collapse as an instantaneous physical event. It is better to think of it as an update of our knowledge about the physical system.