Weak coupling expansion of the low-lying energy values in SU(3) gauge theory on a torus

Weisz, Peter; Ziemann, Volker

doi:10.1016/0550-3213(87)90031-9

Cited by 37 publications

(40 citation statements)

References 18 publications

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“…Subsequently the lowest energy levels of SU(2) [2] and SU(3) [3] gauge theories in small volumes were computed by using this Hamiltonian. Van Baal and Koller then found that the crucial tunnelling between degenerate vacuua can be obtained by imposing appropriate nonperturbative boundary conditions on the Raleigh-Ritz trial wave functions [4].…”

Section: Introductionmentioning

confidence: 99%

“…Results In Intermediate Volumes (0.24 < z κ < 1. 3) In this part we will show that our lattices with β > β c belong to the intermediate volume region. Since in this region our string tension data have large error bars, we just simply use the string tension data of ref.…”

Section: Su (2) Gauge Theory In Finite Volumes At T B ≈mentioning

confidence: 99%

“…where P ( r) ≡ 1 2 T r Na τ =1 U a ( r, τ ), is the Polyakov loop closed in the N a direction and ✷ µν = 1 2 T r(U P ) is the plaquette variable with the orientation (µ, ν), which has 6 different values, (µ, ν)=(2, 3), (1,3), (1,2), (1,4), (2,4), (3,4).…”

Section: Measurements Of the Flux Distributionsmentioning

confidence: 99%

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SU(2) flux distributions on finite lattices

Peng

Haymaker

1993

Phys. Rev. D

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We studied SU (2) flux distributions on four dimensional Euclidean lattices with one dimension very large. By choosing the time direction appropriately we can study physics in two cases: one is finite volume in the zero temperature limit, another is finite temperature in the intermediate to large volume limit.We found that for cases of β > β c there is no intrinsic string formation. Our lattices with β > β c belong to the intermediate volume region, and the string tension in this region is due to finite volume effects. In large volumes we found evidence for intrinsic string formation.

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Section: Introductionmentioning

confidence: 99%

Section: Su (2) Gauge Theory In Finite Volumes At T B ≈mentioning

confidence: 99%

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SU(2) flux distributions on finite lattices

Peng

Haymaker

1993

Phys. Rev. D

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“…For pure gauge fields the spectrum was determined by variational methods for SU(2) and SU(3) in small 13-51 and intermediate volumes [2,11,12]. In the case of SU(3) in a small volume [4,5] the number of basis functions for the variational method was rather small for some states. As is well known.…”

Section: I* Introductionmentioning

confidence: 99%

Spectrum of the effective SU(3) Hamiltonian in a small volume computed by path-integral Monte Carlo integration

Tiedemann

1991

Phys. Rev. D

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Using a simple Monte Carlo integration method for quantum-mechanical problems on a "time lattice" the mass gaps of the low-lying states of Liischer's effective Hamiltonian with and without massless fermions for a small volume are computed. While there is good agreement between this method and previous Rayleigh-Ritz-type calculations in the case of SU(2), notable differences are found in the case of SU(3) for most states. The statistical and systematic errors are competitive with those of the variational method. Having no dependence on basis set size, the Monte Carlo method is a good alternative to the Rayleigh-Ritz calculations also for SU(3). An extension of the method to intermediate volumes including fermions is definitely possible.

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“…(1.5)-(1.6) for the case of Yang-Mills quantum mechanics of spatially constant gluon fields, has been found in [2] for SU (2) and in [3] for SU (3), in the context of a weak coupling expansion in g 2/3 , using the variational approach with gauge-invariant wave-functionals automatically satisfying (1.6). The corresponding unconstrained approach, a description in terms of gauge-invariant dynamical variables via an exact implementation of the Gaws laws, has been considered by many authors (o.a.…”

Section: Introductionmentioning

confidence: 99%

QCD in terms of gauge-invariant dynamical variables

Pavel¹

2013

Proceedings of XTH Quark Confinement and the Hadron Spectrum — PoS(Confinement X)

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For a complete description of the physical properties of low-energy QCD, it might be advantageous to first reformulate QCD in terms of gauge-invariant dynamical variables, before applying any approximation schemes. Using a canonical transformation of the dynamical variables, which Abelianises the non-Abelian Gauss-law constraints to be implemented, such a reformulation can be achieved for QCD. The exact implementation of the Gauss laws reduces the colored spin-1 gluons and spin-1/2 quarks to unconstrained colorless spin-0, spin-1, spin-2 and spin-3 glueball fields and colorless Rarita-Schwinger fields respectively. The obtained physical Hamiltonian can then be rewritten into a form, which separates the rotational from the scalar degrees of freedom, and admits a systematic strong-coupling expansion in powers of λ = g −2/3 , equivalent to an expansion in the number of spatial derivatives. The leading-order term in this expansion corresponds to non-interacting hybrid-glueballs, whose low-lying masses can be calculated with high accuracy by solving the Schrödinger-equation of the Dirac-Yang-Mills quantum mechanics of spatially constant physical fields (at the moment only for the 2-color case). Due to the presence of classical zero-energy valleys of the chromomagnetic potential for two arbitrarily large classical glueball fields (the unconstrained analogs of the well-known constant Abelian fields), practically all glueball excitation energy is expected to go into the increase of the strengths of these two fields. Higher-order terms in λ lead to interactions between the hybrid-glueballs and can be taken into account systematically using perturbation theory in λ . Xth Quark Confinement and the Hadron Spectrum

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Weak coupling expansion of the low-lying energy values in SU(3) gauge theory on a torus

Cited by 37 publications

References 18 publications

SU(2) flux distributions on finite lattices

SU(2) flux distributions on finite lattices

Spectrum of the effective SU(3) Hamiltonian in a small volume computed by path-integral Monte Carlo integration

QCD in terms of gauge-invariant dynamical variables

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