Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks

• URL: http://arxiv.org/abs/2212.04490v1
• Date: Thu, 8 Dec 2022 18:57:47 GMT
• Title: Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks
• Authors: Saurabh V. Kadam, Indrakshi Raychowdhury, and Jesse R. Stryker
• Abstract summary: We present a loop-string-hadron (LSH) framework in 1+1 dimensions for describing the dynamics of SU(3) gauge fields coupled to staggered fermions. The LSH approach uses gauge invariant degrees of freedoms such as loop (segments), string (ends), and hadrons, is free of all nonabelian gauge redundancy, and is described by a Hamiltonian containing only local interactions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Towards the goal of quantum computing for lattice quantum chromodynamics, we present a loop-string-hadron (LSH) framework in 1+1 dimensions for describing the dynamics of SU(3) gauge fields coupled to staggered fermions. This novel framework was previously developed for SU(2) lattice gauge theory in $d\leq3$ spatial dimensions and its advantages for classical and quantum algorithms have thus far been demonstrated in $d=1$. The LSH approach uses gauge invariant degrees of freedoms such as loop (segments), string (ends), and hadrons, is free of all nonabelian gauge redundancy, and is described by a Hamiltonian containing only local interactions. In this work, the SU(3) LSH framework is systematically derived from the reformulation of Hamiltonian lattice gauge theory in terms of irreducible Schwinger bosons (Anishetty et al., J. Phys. A: Math. Theor. 43 (2010) 035403), including the addition of staggered quarks. Furthermore, the superselection rules governing the LSH dynamics are identified directly from the form of the Hamiltonian. The SU(3) LSH Hamiltonian with open boundary conditions has been numerically confirmed to agree with the completely gauge-fixed Hamiltonian, which contains long-range interactions and does not generalize to either periodic conditions or to $d>1$.

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