Abstract
We discuss lattice QCD with one flavor of staggered fermions and show that in the path integral the baryon contributions can be fully separated from quark and diquark contributions. The baryonic degrees of freedom (d.o.f.) are independent of the gauge field, and the corresponding free fermion action describes the baryons through the joint propagation of three quarks. The nonbaryonic dynamics is described by quark and diquark terms that couple to the gauge field. When evaluating the quark and diquark contributions in the strong coupling limit, the partition function completely factorizes into baryon bags and a complementary domain. Baryon bags are regions in space-time where the dynamics is described by a single free fermion made out of three quarks propagating coherently as a baryon. Outside the baryon bags, the relevant d.o.f. are monomers and dimers for quarks and diquarks. The partition sum is a sum over all baryon bag configurations, and for each bag, a free fermion determinant appears as a weight factor.
Highlights
The path integral of a quantum field theory usually can be represented in several ways that may highlight different properties of the theory or allow for different computational approaches
Several interesting results were obtained for strong coupling QCD [7–17] with this type of representations, and related expansion techniques for fermions were used in various suggestions for a fully dualized version of lattice QCD [18–22]
Worldline techniques play a prominent role in purely fermionic lattice field theories with fermionic self-interaction terms. For some of these theories, it is possible to work with so-called fermion bags, which are domains on the lattice where the dynamics is essentially described by free fermions
Summary
The path integral of a quantum field theory usually can be represented in several ways that may highlight different properties of the theory or allow for different computational approaches. Several interesting results were obtained for strong coupling QCD [7–17] with this type of representations, and related expansion techniques for fermions were used in various suggestions for a fully dualized version of lattice QCD [18–22]. Worldline techniques play a prominent role in purely fermionic lattice field theories with fermionic self-interaction terms. For some of these theories, it is possible to work with so-called fermion bags, which are domains on the lattice where the dynamics is essentially described by free fermions. Quarks and diquarks are the relevant d.o.f. The form of the baryon bag representation which we find for the strong coupling limit can be viewed as a variant of the loop-dimer-monomer representation [5,6], where classes of contributions are resummed into the baryon bags. We show that the corresponding weights can be written as fermion determinants for a free Dirac operator restricted to the respective baryon bag
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