Is there a relationship between Yang-Mills mass gap and zero point energy? Explain.

Yang–Mills Existence and Mass Gap. Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on R 4 {\\displaystyle \\mathbb {R} ^{4}} and has a mass gap Δ > 0. Existence includes establishing axiomatic properties at least as strong as those cited in Streater & Wightman (1964), Osterwalder & Schrader (1973) and Osterwalder & Schrader (1975).

 

In this statement, a Yang–Mills theory is a non-Abelian quantum field theory similar to that underlying the Standard Model of particle physics; R 4 {\\displaystyle \\mathbb {R} ^{4}} is Euclidean 4-space; the mass gap Δ is the mass of the least massive particle predicted by the theory.

 

Therefore, the winner must prove that:

Yang–Mills theory exists and satisfies the standard of rigor that characterizes contemporary mathematical physics, in particular constructive quantum field theory

 It must have a “mass gap;” namely there must be some constant ∆ > 0 such that every excitation of the vacuum has energy at least ∆.

 It must have “quark confinement,” that is, even though the theory is describedintermsofelementaryfields, suchasthequarkfields, thattransform non-trivially under SU(3), the physical particle states—such as the proton, neutron, and pion—are SU(3)-invariant.

 It must have “chiral symmetry breaking,” which means that the vacuum is potentially invariant (in the limit, that the quark-bare masses vanish) only under a certain subgroup of the full symmetry group that acts on the quark fields.