Measure of the path integral in lattice gauge theory

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

doi:10.1103/physrevd.71.077502

Cited by 2 publications

(3 citation statements)

References 5 publications

(5 reference statements)

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“…The effective interaction terms in the Lagrangian which appear due to the presence of the Haar measure have been discussed earlier in QCD (see [43] and references therein).…”

Section: B Pion Field Parameterization In Chiral Sigma Modelmentioning

confidence: 99%

Underlying Gauge Symmetries of Second-Class Constraints Systems

Krivoruchenko

Faessler

Râduţâ

et al. 2007

Int. J. Mod. Phys. A

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Gauge-invariant systems in unconstrained configuration and phase spaces, equivalent to secondclass constraints systems upon a gauge-fixing, are discussed. A mathematical pendulum on an n − 1-dimensional sphere S n−1 as an example of a mechanical second-class constraints system and the O(n) non-linear sigma model as an example of a field theory under second-class constraints are discussed in details and quantized using the existence of underlying dilatation gauge symmetry and by solving the constraint equations explicitly. The underlying gauge symmetries involve, in general, velocity dependent gauge transformations and new auxiliary variables in extended configuration space. Systems under second-class holonomic constraints have gauge-invariant counterparts within original configuration and phase spaces. The Dirac's supplementary conditions for wave functions of first-class constraints systems are formulated in terms of the Wigner functions which admit, as we show, a broad set of physically equivalent supplementary conditions. Their concrete form depends on the manner the Wigner functions are extrapolated from the constraint submanifolds into the whole phase space.

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“…The effective interaction terms in the Lagrangian which appear due to the presence of the Haar measure have been discussed earlier in QCD (see [43] and references therein).…”

Section: B Pion Field Parameterization In Chiral Sigma Modelmentioning

confidence: 99%

Underlying Gauge Symmetries of Second-Class Constraints Systems

Krivoruchenko

Faessler

Râduţâ

et al. 2007

Int. J. Mod. Phys. A

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“…(35) goes over to δ(U fi − U in ), as should be. A numerical simulation [47] has shown that in lattice gauge theory (with non-zero a 0 ) also the sub-leading term is important and can not be neglected.…”

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

confidence: 99%

“…In the case of U(1) lattice gauge theory, such normalization factor has been computed in Ref. [47]. It is given as follows.…”

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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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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Measure of the path integral in lattice gauge theory

Cited by 2 publications

References 5 publications

Underlying Gauge Symmetries of Second-Class Constraints Systems

Underlying Gauge Symmetries of Second-Class Constraints Systems

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

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Measure of the path integral in lattice gauge theory

Cited by 2 publications

References 5 publications

Underlying Gauge Symmetries of Second-Class Constraints Systems

Underlying Gauge Symmetries of Second-Class Constraints Systems

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