Formulating light cone QCD on the lattice

Grünewald, D.; Ilgenfritz, Ernst-Michael; Prokhvatilov, E. V.; Pirner, Hans J.

doi:10.1103/physrevd.77.014512

Cited by 13 publications

(32 citation statements)

References 36 publications

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“…Hamiltonian light-front field theory in a discretized momentum basis [1] and in transverse lattice approaches [2][3][4] have shown significant promise. Here a basis-function approach is presented that exploits recent advances in solving the nonrelativistic strongly interacting nuclear many-body problem [5,6].…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian light-front field theory in a basis function approach

et al. 2010

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Hamiltonian light-front quantum field theory constitutes a framework for the non-perturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing the light-front gauge and adopting a basis function representation, we obtain a large, sparse, Hamiltonian matrix for mass eigenstates of gauge theories that is solvable by adapting the ab initio no-core methods of nuclear many-body theory. Full covariance is recovered in the continuum limit, the infinite matrix limit. There is considerable freedom in the choice of the orthonormal and complete set of basis functions with convenience and convergence rates providing key considerations. Here, we use a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall AdS/QCD model obtained from light-front holography. We outline our approach and present illustrative features of some non-interacting systems in a cavity. We illustrate the first steps towards solving QED by obtaining the mass eigenstates of an electron in a cavity in small basis spaces and discuss the computational challenges.Comment: 35 pages, 15 figures, Revised to correct Fig. 7 and add new Fig. 15 with spectral results for electron in a transverse cavit

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Section: Introductionmentioning

confidence: 99%

Hamiltonian light-front field theory in a basis function approach

et al. 2010

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“…light-front QED wave equations for the electron plus electron-photon system [21,22,23] 2. simplified gauge theories with a transverse lattice [2,3,24] 3. Hamiltonian QED for the electron plus electron-photon system in a trap with a basis function approach [4,5] and without a trap [8,25].…”

Section: Light-front Hamiltonian Field Theorymentioning

confidence: 99%

“…For background, one notes that Hamiltonian light-front field theory in a discretized momentum basis [1] and in transverse lattice approaches [2,3] have shown significant promise. I outline here a Hamiltonian basis function approach following Refs.…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian Light-Front Field Theory: Recent Progress and Tantalizing Prospects

Vary

2011

Few-Body Syst

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Fundamental theories, such as Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD) promise great predictive power addressing phenomena over vast scales from the microscopic to cosmic scales. However, new non-perturbative tools are required for physics to span from one scale to the next. I outline recent theoretical and computational progress to build these bridges and provide illustrative results for Hamiltonian Light Front Field Theory. One key area is our development of basis function approaches that cast the theory as a Hamiltonian matrix problem while preserving a maximal set of symmetries. Regulating the theory with an external field that can be removed to obtain the continuum limit offers additional possibilities as seen in an application to the anomalous magnetic moment of the electron. Recent progress capitalizes on algorithm and computer developments for setting up and solving very large sparse matrix eigenvalue problems. Matrices with dimensions of 20 billion basis states are now solved on leadership-class computers for their low-lying eigenstates and eigenfunctions.

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“…In Ref. [9] we have constructed a ground state wave functional of the nlc Hamiltonian which is simpler than the ground state in equal-time theory. In Ref.…”

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confidence: 99%

Gluon Structure Function in Hamiltonian Lattice QCD

Pirner¹,

Gruenewald²,

Ilgenfritz³

2010

Proceedings of Light Cone 2010: Relativistic Hadronic and Particle Physics — PoS(LC2010)

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We calculate the gluon structure function of a color dipole in a new approach evaluating the matrix elements of SU(2) gluon field operators separated along a direction close to the light cone. As vacuum state in the pure glue sector, we use a variational ground state of the near-light-cone Hamiltonian. With a mean momentum fraction of the gluons fixed to the "experimental value" in a proton, the resulting gluon structure function for a dipole state with four links is compared qualitatively to the NLO MRST 2002 parameterization at Q 2 = 1.5 GeV 2 .

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Formulating light cone QCD on the lattice

Cited by 13 publications

References 36 publications

Hamiltonian light-front field theory in a basis function approach

Hamiltonian light-front field theory in a basis function approach

Hamiltonian Light-Front Field Theory: Recent Progress and Tantalizing Prospects

Gluon Structure Function in Hamiltonian Lattice QCD

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