Existence of mesons and mass splitting in strong coupling lattice quantum chromodynamics.

We consider one flavor lattice quantum chromodynamics in theimaginary time functional integral formulation for space dimensions d=2, 3 with 4×4 Dirac spin matrices, small hopping parameter κ, 0<κ<1, and zero plaquette coupling. We determine the energy-momentum spectrum associated with four-component gauge invariant local meson fields which are composites of a quark and an antiquark field. For the associated correlation functions, we establish a Feynman–Kac formula and a spectral representation. Using this representation, we show that the mass spectrum consists of two distinct masses m[sub a] and m[sub b], given by m[sub c]=-2 ln κ+r[sub c](κ), c=a,b, where r[sub c] is real analytic. For d=2, m[sub a] and m[sub b] have multiplicity two and the mass splitting is κ[sup 4]+O(κ[sup 6]); for d=3, one mass has multiplicity one and the other three, with mass splitting 2κ[sup 4]+O(κ[sup 6]). In the subspace of the Hilbert space generated by an even number of fermion fields the dispersion curves are isolated (upper gap property) up to near the two-meson threshold of asymptotic mass -4 ln κ. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]