The authors present a comprehensive framework for formulating Hamiltonian lattice gauge theory (HLGT) on general graphs, with a focus on the application of the Loop-String-Hadron (LSH) formulation.
The key steps are:
Maximal Tree Gauge Fixing: The authors show how HLGT on a lattice can be reformulated in terms of a "flower" graph, where all but a few links have been gauge-fixed to the identity. This reduces the gauge redundancy to a single vertex.
Point Splitting: By applying point splitting, the high-valency vertex of the flower can be transformed into a "branch" structure, where the axis-angle degrees of freedom are separated onto different parts of the graph.
LSH Formulation: The authors develop the prepotential formulation and construct gauge-invariant operators, such as loop operators and Wilson line operators, in terms of Schwinger bosons. This allows them to write the fully gauge-fixed Hamiltonian using these LSH operators.
Examples: The authors provide simple examples of the one-plaquette and two-plaquette systems to illustrate the LSH formulation on the branch structure.
The main contribution is the development of a gauge-invariant LSH formulation on general graphs, which provides a systematic way to construct the Hilbert space and Hamiltonian of HLGT in the weak coupling limit.
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by I. M. Burban... at arxiv.org 10-01-2024
https://arxiv.org/pdf/2409.13812.pdfDeeper Inquiries