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The Schr\"odinger Functional for Improved Gluon and Quark Actions
High Energy Physics - Lattice · Submitted 21 May 1997
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our ultimate aim is the construction of actions that allow accurate simulations of all aspects of QCD on coarse lattices.
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The abstract, sentence by sentence
The Schr\"odinger Functional (quantum/lattice field theory with Dirichlet boundary conditions) is a powerful tool in the non-perturbative improvement and for the study of other aspects of lattice QCD. Here we adapt it to improved gluon and quark actions, on isotropic as well as anisotropic lattices. Specifically, we describe the structure of the boundary layers, obtain the exact form of the classically improved gauge action, and outline the modifications necessary on the quantum level. The projector structure of Wilson-type quark actions determines which field components can be specified at the boundaries. We derive the form of O(a) improved quark actions and describe how the coefficients can be tuned non-perturbatively. There is one coefficient to be tuned for an isotropic lattice, three in the anisotropic case. Our ultimate aim is the construction of actions that allow accurate simulations of all aspects of QCD on coarse lattices.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The Schr\"odinger Functional (quantum/lattice field theory with Dirichlet boundary conditions) is a powerful tool in the non-perturbative improvement and for the study of other aspects of lattice QCD. | background 1.00 | 0.06 | 0.07 | asserted 1.00 |
| s1 | Here we adapt it to improved gluon and quark actions, on isotropic as well as anisotropic lattices. | contribution 0.99 | 0.92 | 0.06 | asserted 0.99 |
| s2 | Specifically, we describe the structure of the boundary layers, obtain the exact form of the classically improved gauge action, and outline the modifications necessary on the quantum level. | contribution 0.94 | 0.93 | 0.08 | asserted 0.99 |
| s3 | The projector structure of Wilson-type quark actions determines which field components can be specified at the boundaries. | background 0.78 | 0.18 | 0.04 | asserted 1.00 |
| s4 | We derive the form of O(a) improved quark actions and describe how the coefficients can be tuned non-perturbatively. | contribution 0.90 | 0.94 | 0.11 | asserted 1.00 |
| s5 | There is one coefficient to be tuned for an isotropic lattice, three in the anisotropic case. | result 0.80 | 0.66 | 0.06 | asserted 1.00 |
| s6 | Our ultimate aim is the construction of actions that allow accurate simulations of all aspects of QCD on coarse lattices. | future work 0.97 | 0.15 | 0.30 | asserted 0.81 |
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The paper
Original abstract
The Schr\"odinger Functional (quantum/lattice field theory with Dirichlet boundary conditions) is a powerful tool in the non-perturbative improvement and for the study of other aspects of lattice QCD. Here we adapt it to improved gluon and quark actions, on isotropic as well as anisotropic lattices. Specifically, we describe the structure of the boundary layers, obtain the exact form of the classically improved gauge action, and outline the modifications necessary on the quantum level. The projector structure of Wilson-type quark actions determines which field components can be specified at the boundaries. We derive the form of O(a) improved quark actions and describe how the coefficients can be tuned non-perturbatively. There is one coefficient to be tuned for an isotropic lattice, three in the anisotropic case. Our ultimate aim is the construction of actions that allow accurate simulations of all aspects of QCD on coarse lattices.
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References
How the literature uses it
3 arXiv papers cite this in 4 sentences
Papers citing it · 1 sentence without a confident label
Uses its method or tool 1 paper
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As we have an extended gauge action (rather than the simpler Wilson gluon action), we fix two values at each double boundary layer and so we choose, following [ref] [An alternative procedure using single layer boundaries is given in [ref] .], $U^c_μ$ from eq.
Non-perturbative improvement of stout-smeared three flavour clover fermions · The Schrödinger functional · 0.94
Cites it as background 1 paper
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For QCD or QCD-like lattice theories, where the physics at the UV-cutoff scale is for most of the simulation parameter space governed by the gauge action and controlled by the inverse bare gauge coupling, $β_L=2 N/g_0^2$, these boundary conditions are usually well behaved [ref] and can even be further improved [ref] to match bulk actions with reduced UV-cutoff effects [ref] .
Improved Dirichlet boundary conditions for lattice gauge-fermion theories · Homogeneous temporal Dirichlet boundary conditions · 0.80
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