The basis of the physical Hilbert space of lattice gauge theories

Burgio, Giuseppe; Pietri, R. De; Morales‐Técotl, H. A.; Urrutia, L. F.; Vergara, J. David

doi:10.1016/s0550-3213(99)00533-7

Cited by 38 publications

(52 citation statements)

References 20 publications

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“…In such a setup Gauss's law on the states is explicitly resolved with the help of the gauge constraint, without any need to construct the physical Hilbert space explicitly [5]. The results obtained [6] agree with the Gribov-Zwanziger confinement scenario [7][8][9] and with the existence of a confining potential driven by topological excitations [10][11][12].…”

Section: Introductionsupporting

confidence: 63%

Running mass, effective energy, and confinement: The lattice quark propagator in Coulomb gauge

et al. 2012

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We calculate the lattice quark propagator in Coulomb gauge from both dynamical and quenched configurations. We show that in the continuum limit both the static and the full quark propagators are multiplicatively renormalizable. From the propagator we extract the quark renormalization function ZðjpjÞ and the running mass MðjpjÞ and extrapolate the latter to the chiral limit. We find that MðjpjÞ practically coincides with the corresponding Landau gauge function for small momenta. The computation of MðjpjÞ can, however, be made more efficient in Coulomb gauge; this can lead to a better determination of the chiral mass and the quark anomalous dimension. Moreover from the structure of the full propagator we can read an expression for the dispersion relation of quarks, compatible with an IR divergent effective energy. If confirmed on larger volumes, this finding would allow one to extend the Gribov-Zwanziger confinement mechanism to the fermionic sector of QCD.

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Section: Introductionsupporting

confidence: 63%

Running mass, effective energy, and confinement: The lattice quark propagator in Coulomb gauge

et al. 2012

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“…In this work, the angular momentum basis [45,49,50] is utilized, made computationally feasible on quantum devices by exploiting the local gauge symmetry to remove the angular momentum alignment variables. Time evolution of a one-dimensional string of two SU(2) plaquettes is then implemented on IBM's Tokyo [93] quantum device with employed error mitigation techniques.…”

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confidence: 99%

SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers

2020

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An improved mapping of one-dimensional SU(2) non-Abelian gauge theory onto qubit degrees of freedom is presented. This new mapping allows for a reduced unphysical Hilbert space. Insensitivity to interactions within this unphysical space is exploited to design more efficient quantum circuits. Local gauge symmetry is used to analytically incorporate the angular momentum alignment, leading to qubit registers encoding the total angular momentum on each link. The results of a multiplaquette calculation on IBM's quantum hardware are presented.

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“…This can be generalized to non-Abelian gauge symmetry. For example, Burgio et al [51] have shown how to construct a gauge invariant Hilbert space for the gauge group SU(2). irreducible representation characterized by index (set) {ν} is given by a matrix…”

Section: Discussionmentioning

confidence: 99%

SPECTRUM AND WAVE FUNCTIONS OF U(1)₂₊₁ LATTICE GAUGE THEORY FROM MONTE CARLO HAMILTONIAN

Hosseinizadeh

Kröger

Melkonyan³

et al. 2011

Mod. Phys. Lett. A

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We address an old problem in lattice gauge theory -the computation of the spectrum and wave functions of excited states. Our method is based on the Hamiltonian formulation of lattice gauge theory. As strategy, we propose to construct a stochastic basis of Bargmann link states, drawn from a physical probability density distribution. Then we compute transition amplitudes between stochastic basis states. From a matrix of transition elements we extract energy spectra and wave functions. We apply this method to U(1) 2+1 lattice gauge theory. We test the method by computing the energy spectrum, wave functions and thermodynamical functions of the electric Hamiltonian of this theory and compare them with analytical results. We observe a reasonable scaling of energies and wave functions in the variable of time. We also present first results on a small lattice for the full Hamiltonian including the magnetic term.

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The basis of the physical Hilbert space of lattice gauge theories

Cited by 38 publications

References 20 publications

Running mass, effective energy, and confinement: The lattice quark propagator in Coulomb gauge

Running mass, effective energy, and confinement: The lattice quark propagator in Coulomb gauge

SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers

SPECTRUM AND WAVE FUNCTIONS OF U(1)₂₊₁ LATTICE GAUGE THEORY FROM MONTE CARLO HAMILTONIAN

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The basis of the physical Hilbert space of lattice gauge theories

Cited by 38 publications

References 20 publications

Running mass, effective energy, and confinement: The lattice quark propagator in Coulomb gauge

Running mass, effective energy, and confinement: The lattice quark propagator in Coulomb gauge

SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers

SPECTRUM AND WAVE FUNCTIONS OF U(1)2+1 LATTICE GAUGE THEORY FROM MONTE CARLO HAMILTONIAN

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SPECTRUM AND WAVE FUNCTIONS OF U(1)₂₊₁ LATTICE GAUGE THEORY FROM MONTE CARLO HAMILTONIAN