Is the QFT field real or just a mathematical tool?

[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.