papalex on Nostr: And while John is of course right about his diagnosis about the SM, I think in the ...

And while John is of course right about his diagnosis about the SM, I think in the particular case of this post one could make a mathsy phrasing of what the "soup of quarks" means. Let me have a try at it.

Original: "protons and neutrons act like bags full of a soup [...] In the quark condensate, the clockwise spinning virtual quarks are entangled with counterclockwise spinning virtual antiquarks."

Mathsify: "SM Quarks are a local excitation in a 𝔰𝔲(3)⊕𝔰𝔲(2)⊕𝔲(1)-gauge 𝔰𝔬(3,1)-spinor bundle with respect to the fundamental representation. But they do not appear as isolated excitation because the Hamiltonian / Lagrangian (aka dynamics) prohibits this (strong coupling). Protons and Neutrons are a fairly stable form of a collective excitation. One can expand it in terms of representations using three fundamental representations (three quarks) but the dynamics makes things complicated, due to frustration of constraints (quark confinement versus charge repulsion etc). This has the effect of adding a whole bunch of virtual representations to the mix (i.e. the decomposition into three fundamental representations is not that clean but really there is a bit more than just that, and this "bit more" is not a clean representation but a superposition of things => the condensate). This has the effect of both, breaking the symmetry between the different Weyl sectors of the spinor bundle and of increasing the mass from the Higgs mass of the three quarks."

This is still only somewhat mathsy. I would be curious how to make this even sharper John Carlos Baez (npub1nf4…nqe4)?