Undergrad Is the QFT field real or just a mathematical tool?

[meopemuk]

@
meopemuk

I have been looking at your work, and surprisingly I saw you are looking at my thread. can you comment please.

There is a legitimate point of view that quantum fields are not those all-penetrating substances, but simply abstract mathematical constructs (linear combinations of particle creation and annihilation operators). The chief reason for introducing these linear combinations is to simplify building Poincare-invariant interaction operators between particles. Indeed, in many cases one can show that simple polynomials of quantum fields can serve as interaction operators satisfying all Poincare commutators. This goal is very difficult (but possible) to reach without the help of quantum fields.

I've learned this point of view from Weinberg's textbook, vol. 1.

Eugene.

 

[ftr]

There is a legitimate point of view that quantum fields are not those all-penetrating substances, but simply abstract mathematical constructs (linear combinations of particle creation and annihilation operators). The chief reason for introducing these linear combinations is to simplify building Poincare-invariant interaction operators between particles. Indeed, in many cases one can show that simple polynomials of quantum fields can serve as interaction operators satisfying all Poincare commutators. This goal is very difficult (but possible) to reach without the help of quantum fields.

I've learned this point of view from Weinberg's textbook, vol. 1.

Eugene.

Thanks.

I have some questions
1. since your theory is "action at distance", have you thought how to solve the EPR problem?
2. what is "virtual particle" equivalence in your theory?

 

[meopemuk]

Thanks.

I have some questions
1. since your theory is "action at distance", have you thought how to solve the EPR problem?
2. what is "virtual particle" equivalence in your theory?

1. I don't think there is any physical problem with EPR experiment. The related discussions are heavily philosophical and don't belong to this thread.
2. Most physicists will tell you that virtual particles exist only on paper in the form of internal lines in Feynman diagrams. The purpose of these lines is to indicate certain factors in integrals. There is nothing more to them.

Eugene.

 

[ftr]

1. I don't think there is any physical problem with EPR experiment. The related discussions are heavily philosophical and don't belong to this thread.
2. Most physicists will tell you that virtual particles exist only on paper in the form of internal lines in Feynman diagrams. The purpose of these lines is to indicate certain factors in integrals. There is nothing more to them.

Eugene.

Thanks again
I am not interested in a long discussion about EPR, obviously it is experimentally confirmed. I was just wondering if your theory had anything to say about it or at least it could shed some light since both indicate an action at distance phenomenon. But I understand if you want to stay silent on it.

As for virtual, my question is what is the equivalent in your model,sorry if my question is vague.

 

[jtbell]

In the present situation of a single electron, the field strength is proportional to the spatially probability density, which is calculated in many textbooks. For the ground state it is spherically symmetric and decays exactly exponentially with the distance from the center, hence is maximal there.

Isn't it maximal at Bohr distance? We are talking about hydrogen atom, right?

A. Neumaier is referring to the probability per unit volume (Fig. 3-4 in the following link), whereas you are referring to the probability per unit radial distance from the nucleus (Fig. 3-5).
http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html

 

[EugeneBird]

In his 2012 Salam lecture series, I heard Nima Arkani-Hamed say that you are allowed to re-define the fields when computing a path integral. He made it sound as though there is nothing compelling one to think that the field itself is a part of reality. I'm not knowledgeable enough to understand the results of Googling "path integral field redefinition" - but it seems to generate speculation that quantum fields aren't fundamental - that really there is something deeper and non-local that could be used to compute experimental results without using fields. Search for "amplituhedron".

 

[vanhees71]

I guess the speaker referred to the socalled "equivalence theorem". It says that it doesn't matter which particular field variable lr some function of it you take to evaluate the correlation functions entering the S matrix. You always get the same result. This is understandable since it's the asymptotic behavior that defines particles, i.e., the connection of the asymptotic free in and outstates via the dynamics. For a formal path-integral treatment, see

http://th.physik.uni-frankfurt.de/~hees/publ/lect.pdf
Section 4.6.2

 

[A. Neumaier]

you are allowed to re-define the fields when computing a path integral. He made it sound as though there is nothing compelling one to think that the field itself is a part of reality.

One is also allowed to re-define positions by making a coordinate transformation. But this does not imply that there is nothing compelling one to think that position itself is a part of reality. It only implies that position needs a coordinate system for its description. Whatever one can compute from positions that is invariant under coordinate changes (such as distances between points, angles in a triangle etc. is part of reality.

Essentially the same holds for fields. One may exchange a field by a reexpression of it without altering the physics, but one cannot get rid of the fields themselves. The vector potential appears in the field equations but changes under a gauge transformation. But the electromagnetic field strength computed from it is invariant and has a physical meaning. More generally, one can always replace a field by a linear or nonlinear expression of it - as long as the transformation is invertible, the resulting descriptions are physically equivalent, but the expression for the measurable quantities may become simpler or more complex and must be transformed as well. The choices made in practice are those where the calculations leading to the predictions are simplest. This usually means that the form of the fields is dictated by symmetry principles and renormalization considerations.