Analytic calculation of the vacuum wave function for (2+1)-dimensional SU(2) lattice gauge theory

Guo, Song; Chen, Qi-Zhou; Li, Lei

doi:10.1103/physrevd.49.507

Cited by 43 publications

(96 citation statements)

References 21 publications

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“…The essential feature of our truncation scheme, which differs sufficiently from the scheme in [7], is in the treatment of this second term. It has been generally proven [1] that in the long wavelength limit this term should behave as…”

mentioning

confidence: 99%

“…This equation can be solved by a systematic method [1,2,3,4,5], in which R(U ) is expanded in order of graphs G n,i , i.e.,…”

mentioning

confidence: 99%

“…In [1,2,3,4,5], we developed an efficient eigenvalue equation method with some new truncation schemes which preserve the continuum limit. This is an essential step towards the scaling.…”

mentioning

confidence: 99%

“…One sees that not only graphs of the same order, but also graphs of different orders mix, so that the classification becomes rather involved. In [1,2], the disconnected graphs were taken as independent graphs. We realize that this is not the most efficient way, because the disconnected graphs have large overlapping with graphs of lower orders in the weak coupling region.…”

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confidence: 99%

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Spectroscopy and large scale wave functions

Chen

Guo

Luo³

et al. 1996

Nuclear Physics B - Proceedings Supplements

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We discuss the relevance of long wavelength excitations for the low energy spectrum of QCD, and try to develop an efficient method for solving the Schrödinger equation, and for extracting the glueball masses and long wavelength functions of the ground and excited states. Some technical problems appearing in the calculations of SU(3) gauge theory are discussed.QCD in the pure gauge sector possesses a nontrivial vacuum structure and bound states called glueballs. Solving the Schrödinger equation in the Hamiltonian formulation can directly provide not only the glueball masses from the eigenvalues, but also the profiles, i.e., the wave functions for the ground state and excited states.Strictly speaking, the continuum physics should be extracted in the asymptotic scaling region predicted by the renormalization group equation. In [1, 2, 3, 4, 5], we developed an efficient eigenvalue equation method with some new truncation schemes which preserve the continuum limit. This is an essential step towards the scaling.Our starting point is to obtain the long wavelength wave functions of the ground and excited states. The philosophy is to keep the correct long wavelength limit during the truncation. The low energy spectrum originates mainly from the long wavelength excitations. This is because the size or the Compton length of a glueball, which is usually of the same order as that of a hadron or the lattice size, should be much greater than the lattice spacing a. It is worth mentioning that the confinement of gluons or static quarks is closely related to the long wavelength structure of the vacuum. For the long wavelength configurations U , 1

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mentioning

confidence: 99%

“…This equation can be solved by a systematic method [1,2,3,4,5], in which R(U ) is expanded in order of graphs G n,i , i.e.,…”

mentioning

confidence: 99%

“…In [1,2,3,4,5], we developed an efficient eigenvalue equation method with some new truncation schemes which preserve the continuum limit. This is an essential step towards the scaling.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Spectroscopy and large scale wave functions

Chen

Guo

Luo³

et al. 1996

Nuclear Physics B - Proceedings Supplements

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“…On general grounds and motivated by strong coupling expansions [8] we consider trial wave functions which are expressed by combinations of gauge invariant Wilson loops with unknown coefficients a. Two main issues are addressed: the cost of computing large loops and the practical simultaneous optimization of many parameters a.…”

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confidence: 99%

Wave functions for SU(2) Hamiltonian lattice gauge theory

Beccaria

2000

Phys. Rev. D

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We study four dimensional SU(2) lattice gauge theory in the Hamiltonian formalism by Green's Function Monte Carlo methods. A trial ground state wave function is introduced to improve the configuration sampling and we discuss the interplay between its complexity and the simulation systematic errors. As a case study, we compare the leading strong coupling approximation and an improved 4 parameters wave function with 1 × 1 and 1 × 2 plaquette terms. Our numerical results favors the second option.

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Application of linked-cluster expansions to quantum hamiltonian lattice systems

Zheng

Hamer

Oitmaa

Theory of Spin Lattices and Lattice Gauge Models

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Analytic calculation of the vacuum wave function for (2+1)-dimensional SU(2) lattice gauge theory

Cited by 43 publications

References 21 publications

Spectroscopy and large scale wave functions

Spectroscopy and large scale wave functions

Wave functions for SU(2) Hamiltonian lattice gauge theory

Application of linked-cluster expansions to quantum hamiltonian lattice systems

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