Baryon Tri-local Interpolating Fields

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We systematically investigate tri-local (non-local) three-quark baryon fields with Uₗ(2)*Uᵣ(2) chiral symmetry, according to their Lorentz and isospin (flavor) group representations. We note that they can also be called as "nucleon wave functions" due to this full non-locality. We study their chiral transformation properties and find all the possible chiral multiplets consisting J=1/2 and J=3/2 baryon fields. We find that the axial coupling constant |gₐ| = 5/3 is only for nucleon fields belonging to the chiral representation (1/2,1)+(1,1/2) which contains both nucleon fields and Delta fields. Moreover, all the nucleon fields belonging to this representation have |gₐ| = 5/3.