# If gauge theory is a redundancy in our description of nature, how can there be phenomena which cannot be described without gauge theory?

As I understand it, gauge "symmetry" can be seen as redundancy in our description of nature. For example, quoting from David Tong's gauge theory notes,

Gauge symmetry is, in many ways, an odd foundation on which to build our best theories of physics. It is not a property of Nature, but rather a property of how we choose to describe Nature. Gauge symmetry is, at heart, a redundancy in our description of the world. Yet it is a redundancy that has enormous utility, and brings a subtlety and richness to those theories that enjoy it.

So, in principle, one might think that one could do away with gauge theory, even if that might come at a considerable practical cost.

Yet, if I understand Chap 5.9 of Weinberg Vol. 1 correctly, it is impossible to write down a theory of a massless particle of helicity $$\pm 1$$ as an ordinary 4-vector field, and instead one must use a field which has a "gauge-like" transformation behaviour. (This is also discussed in this PSE post.) Thus, if we want to describe something like a photon, we are forced towards gauge theory.

Naively, these two ideas seem to contradict each other. How can we reconcile them?

• The claims do not contradict each other. Please be explicit about where you think the contradiction is: Note that Weinberg does not say it is completely impossible to write down a theory of a massless particle with helicity 1 without gauge theory, just that it is impossible as the theory of a 4-vector field. Jul 20 '19 at 18:08

It is impossible to write down a theory of a massless particle of helicity $$\pm 1$$ as an ordinary 4-vector field, and instead one must use a field which has a "gauge-like" transformation behaviour. Thus, if we want to describe something like a photon, we are forced towards gauge theory.