I was reading a paper¹, and it states:
" Therefore, the gauge fields themselves cannot be entities of the physical reality, as any observations should be independent of the chosen gauge"
I'm trying to understand what he wanted to say. Because, as far as I know, W bosons and Z bosons ARE PART of the Physical reality as much as photons and electrons.... Someone could help me figure it out what the author was trying to say?
This is just very sloppy language on the paper's part. As you say, gauge bosons are very real and their existence has physically measurable consequences (otherwise, why would we ever waste time talking about them?). (By the way "photons and electrons" are not good examples of non-gauge particles, because photons are also gauge bosons :) .)
The paper just means that the only physically measurable properties of the gauge fields are the gauge-independent ones. For example, a quantity like $\langle A_\mu^a \rangle$ is not physically measurable because its value depends on your choice of gauge. On the other hand, the quantity $\langle \partial_\mu A_\nu - \partial_\nu A_\mu + i g [A_\mu, A_\nu] \rangle$ is gauge invariant and can be directly measured.
It's like (a slightly more complex version of) the fact that the potential energy $U({\bf x})$ is not physically measurable because it is only defined up to an overall additive constant. Only its derivative ${\bf F(x)} = -{\bf \nabla} U({\bf x})$ is physically measurable, but that doesn't mean that the potential energy function has no physical consequence at all. The gauge fields contain some gauge-dependencies which make them not directly physical, but the appropriate derivatives are directly physical.
