Improved Lattice Gauge Field Hamiltonian

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.

30 pages, LaTeX

References in corpus (10)

• Perfect lattice action for asymptotically free theories
• Efficient glueball simulations on anisotropic lattices
• Lattice QCD on Small Computers
• Instantons from over-improved cooling
• Improved Hamiltonian for Minkowski Yang-Mills Theory
• Redesigning Lattice QCD
• Estimate for the $0^{++}$ glueball mass in QCD
• The Coupled Cluster Method in Hamiltonian Lattice Field Theory
• Glueball Masses in Quantum Chromodynamics
• Universality for SU(2) Yang-Mills Theory in (2+1)D

Cited by in corpus (19)

• Harmonic Oscillator Prepotentials in SU(2) Lattice Gauge Theory
• Monte Carlo study of glueball masses in the Hamiltonian limit of SU(3) lattice gauge theory
• Quantum algorithms for transport coefficients in gauge theories
• Improved Hamiltonians for Quantum Simulations
• Exotic mesons from quantum chromodynamics with improved gluon and quark actions on the anisotropic lattice
• Lattice Renormalization of Quantum Simulations
• The spectrum of qubitized QCD: glueballs in a $S(1080)$ gauge theory
• Gauge Theory Couplings on Anisotropic Lattices
• Gluon Digitization via Character Expansion for Quantum Computers
• Direct Improvement of Hamiltonian Lattice Gauge Theory
• Improved Honeycomb and Hyperhoneycomb Lattice Hamiltonians for Quantum Simulations of Non-Abelian Gauge Theories
• Wave functions for Hamiltonian Lattice Gauge Theory
• Improved lattice QCD with quarks: the 2 dimensional case
• An Analytic Variational Study of the Mass Spectrum in 2+1 Dimensional SU(3) Hamiltonian Lattice Gauge Theory
• Improving the Lattice QCD Hamiltonian
• The Coupled Cluster Method in Hamiltonian Lattice Field Theory: SU(2) Glueballs
• Approximated seventh order calculation of vacuum wave function of 2+1 dimensional SU(2) lattice gauge theory
• Low-lying meson spectrum of large $N_C$ strongly coupled lattice QCD
• Improved Hamiltonian Lattice Gauge Theory