Monte Carlo Hamiltonian of Lattice Gauge Theory

Paradis, F.; Kröger, H.; Luo, Xiang-Qian; Moriarty, K.J.M.

doi:10.1142/s0217732307023146

Cited by 3 publications

(4 citation statements)

References 5 publications

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“…In field theory, the Monte Carlo Hamiltonian has been applied to the (1+1) KleinGordon model for the computation of the spectrum and thermodynamical functions [13][14][15][16], and likewise to the (1+1) scalar model for the computation of the spectrum and thermodynamical functions [17][18][19]. A first step towards the Monte Carlo Hamiltonian in lattice gauge theory has been made in [20] by computing transition amplitudes of U(1) gauge theory.…”

Section: Exp[−h T/h] |ξ ∼ Lim T→∞ Exp[−e Gr T/h]|ω ω|ξ (2)mentioning

confidence: 99%

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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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Section: Exp[−h T/h] |ξ ∼ Lim T→∞ Exp[−e Gr T/h]|ω ω|ξ (2)mentioning

confidence: 99%

“…In quantum mechanics the scalar product x|p can be computed from the commutator [X,P] = ih. Likewise, the scalar product λ|U can be obtained from the commutator [20] [l,Û] = −Û .…”

Section: U(1) 2+1 Lattice Gauge Theorymentioning

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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“…The transition from the flux string basis to the link basis is determined by the commutator [ l, Û ] = − Û and yields [17] < λ|U >= (U ) λ .…”

Section: U (1)2+1 Lattice Gauge Theorymentioning

confidence: 99%

“…In field theory, the Monte Carlo Hamiltonian has been applied to the 1+1 Klein-Gordon model for the computation of the spectrum and thermodynamical functions [10,11,12,13], and likewise to the 1 + 1 scalar model for the computation of the spectrum and thermodynamical functions [14,15,16]. A first step towards the Monte Carlo Hamiltonian in lattice gauge theory has been made in [17] by computing transition amplitudes of U (1) gauge theory. Here we construct the Monte Carlo Hamiltonian for U (1) 2+1 lattice gauge theory and apply it to compute the energy spectrum of excited states, the corresponding wave functions and thermodynamical functions.…”

Section: Introductionmentioning

confidence: 99%

Spectrum and Wave Functions of Excited States in Lattice Gauge Theory

Kröger¹,

Hosseinizadeh²,

Laprise³

et al. 2009

Proceedings of the XXVI International Symposium on Lattice Field Theory — PoS(LATTICE 2008)

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We suggest a new method to compute the spectrum and wave functions of excited states. We construct a stochastic basis of Bargmann link states, drawn from a physical probability density distribution and compute transition amplitudes between stochastic basis states. From such transition matrix we extract wave functions and the energy spectrum. We apply this method to U(1) 2+1 lattice gauge theory. As a test we compute the energy spectrum, wave functions and thermodynamical functions of the electric Hamiltonian and compare it with analytical results. We find excellent agreement. We observe 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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Spectrum and Wave Functions of Excited States in Lattice Gauge Theory

Kröger¹,

Hosseinizadeh²,

Laprise³

et al. 2009

Preprint

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Monte Carlo Hamiltonian of Lattice Gauge Theory

Abstract: We discuss how the concept of the Monte Carlo Hamiltonian can be applied to lattice gauge theories.

Cited by 3 publications

References 5 publications

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

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

Spectrum and Wave Functions of Excited States in Lattice Gauge Theory

Spectrum and Wave Functions of Excited States in Lattice Gauge Theory

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Monte Carlo Hamiltonian of Lattice Gauge Theory

Abstract: We discuss how the concept of the Monte Carlo Hamiltonian can be applied to lattice gauge theories.

Cited by 3 publications

References 5 publications

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

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

Spectrum and Wave Functions of Excited States in Lattice Gauge Theory

Spectrum and Wave Functions of Excited States in Lattice Gauge Theory

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Product

Resources

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

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