Misconceptions about Virtual Particles - Comments

[vanhees71]

Yes, and it's important to keep in mind, upon which real observations our knowledge about things like "galaxies too distant" and the "deep interior of the Earth or the Sun" are used to infer this knowledge about these things we cannot directly observe.

The point is that physics is about what's observable and which conclusions you can draw about what's not directly observable from what we think are universally valid natural laws. It's not about what "reality" might be, because that's something which is not part of the natural sciences, but we are already drifting away again in this direction, which I'd like to avoid.

 

[Tendex]

Microcausality and Hamiltonians are associated with field operators, not with propagators. The mathematical properties of the latter are derived from the former, not vice versa.

Oh my goodness, the propagator involves the product of field operators! Those properties are associated with the commutator for spacelike intervals and with non-perturbative tree level(classical limit) propagation amplitudes for quantized relativistic fields that requires certain boundary condition for its time-ordering evolution operator. Your remark(which I will borrow as a clear example of a moronic truism for my classes) confirms my suspicion that you don't understand neither the physics nor the math of the Lorentz invariant Green function already at nonperturbative tree level. Well, thanks for that.

 

[A. Neumaier]

Oh my goodness, the propagator involves the product of field operators! Those properties are associated with the commutator for spacelike intervals and with non-perturbative tree level(classical limit) propagation amplitudes for quantized relativistic fields that requires certain boundary condition for its time-ordering evolution operator.

The free Feynman propagator is the time-ordered vacuum expectation of a product of two free field operators, yes. Thus it is not a fundamental object but derived from fundamental objects. It is Lorentz invariant because of microcausality, not the other way round. It is useful in scattering theory because for tree diagrams it gives via Feynman rules S-matrix contributions in the Born approximation. Not the other way round.

It is a useful tool, just as powers and factorials are useful tools for computing the exponential function, but the former don"t inherit any of the properties of the latter.

confirms my suspicion that you don't understand neither the physics nor the math of the Lorentz invariant Green function already at nonperturbative tree level.

Didn't you protest against the use of ad hominem attacks?! Practice what you preach!

 

[Tendex]

The free Feynman propagator is the time-ordered vacuum expectation of a product of two free field operators, yes. Thus it is not a fundamental object but derived from fundamental objects. It is Lorentz invariant because of microcausality, not the other way round. It is useful in scattering theory because for tree diagrams it gives via Feynman rules S-matrix contributions in the Born approximation. Not the other way round.

I never implied anything about the other way around. Propagators, whether one considers them fundamental or not are the mathematical objects that ensure those properties by time-ordering correctly the fields.

It is a useful tool, just as powers and factorials are useful tools for computing the exponential function, but the former don"t inherit any of the properties of the latter.

I don't want to enter into your words games about what is fundamental or not. That belongs to your personal subjective philosophy.

Didn't you protest against the use of ad hominem attacks?! Practice what you preach!

I didn't intend it as an attack, just my honest opinion about what's going on here.

 

[A. Neumaier]

Propagators [...] are the mathematical objects that ensure those properties by time-ordering correctly the fields.

No. they are only mathematical objects whose properties are ensured by time-ordering correctly the fields.

Propagators ensure neither microcausality (which requires time-orderability of all correlation functions) nor Lorentz invariance of the free field theory, since without these prerequisites, propagators cannot even be assigned physical meaning.

Both microcausality and Lorentz invariance are guaranteed by constructing free fields as a Fock space over a 1-particle space featuring a unitary positive energy representation of the Poincare group, as discussed in Chapter 3 and 5 of Weinberg's QFT book. Propagators enter the scene only afterwards, in Chapter 6, and heir properties are all deduced from the already established results about free fields.But we seem to differ too much in everything to make a continuation of this exchange fruitful.

 

[fresh_42]

[Moderator's note.]
I have removed the last posts as you are debating in circles, as stated above. Hence this discussion is now at the point to fight for the last word, which is ridiculous. Hence

But we seem to differ too much in everything to make a continuation of this exchange fruitful.

stands and further debate is apparently useless.

In case you prefer to circle some more rounds, please open a separate thread and try to avoid ad hominem arguments.