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Improved Lattice Gauge Field Hamiltonian

Xiang-Qian Luo·Shuo-Hong Guo·H. Kröger·Dieter Schütte
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Abstract

Lepage's improvement scheme is a recent major progress in lattice $QCD$, allowing to obtain continuum physics on very coarse lattices. Here we discuss improvement in the Hamiltonian formulation, and we derive an improved Hamiltonian from a lattice Lagrangian free of $O(a^2)$ errors. We do this by the transfer matrix method, but we also show that the alternative via Legendre transformation gives identical results. We consider classical improvement, tadpole improvement and also the structure of L{ü}scher-Weisz improvement. The resulting color-electric energy is an infinite series, which is expected to be rapidly convergent. For the purpose of practical calculations, we construct a simpler improved Hamiltonian, which includes only nearest-neighbor interactions.

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Xiang-Qian Luo, Shuo-Hong Guo, H. Kröger, Dieter Schütte. 1998-04-22. Improved Lattice Gauge Field Hamiltonian. https://doi.org/10.1103/physrevd.59.034503

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