Chiral perturbation theory in the Schwinger model

Vary, James P.; Fields, T.; Pirner, Hans J.

doi:10.1103/physrevd.53.7231

Cited by 44 publications

(64 citation statements)

References 14 publications

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“…Those investigations are feasible, but would require a higher computational effort. [14] and chiral perturbation theory [16,17]. Fig.2 The dimensionless binding energy of the vector boson versus log 2 (m/g) in the non-relativistic region.…”

Section: Discussionmentioning

confidence: 99%

“…Comparison with chiral perturbation theory [16,17]. Fig.5 Dependence of the dimensionless mass of vector and scalar particle on the θ-angle after subtraction of θ-vacuum energy.…”

Section: Discussionmentioning

confidence: 99%

“…Fig.5 Dependence of the dimensionless mass of vector and scalar particle on the θ-angle after subtraction of θ-vacuum energy. Comparison with chiral perturbation theory [16,17]. …”

Section: Discussionmentioning

confidence: 99%

“…The low lying states of the massive Schwinger model are a vector state and next a scalar state [13,14]. The behaviour in the ultra-relativistic region m/g → 0 has been computed in chiral perturbation theory up to second order by Adam [16] and Vary et al [17]. The vector particle mass behaves as…”

Section: Mass Spectrummentioning

confidence: 99%

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The massive Schwinger model - a Hamiltonian lattice study in a fast moving frame

Kröger

Scheu

1998

Physics Letters B

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We present a non-perturbative study of the massive Schwinger model. We use a Hamiltonian approach, based on a momentum lattice corresponding to a fast moving reference frame, and equal time quantization. We present numerical results for the mass spectrum of the vector and scalar particle. We find good agreement with chiral perturbation theory in the strong coupling regime and also with other non-perturbative studies (Hamer et al., Mo and Perry) in the nonrelativistic regime. The most important new result is the study of the θ-action, and computation of vector and scalar masses as a function of the θ-angle. We find excellent agreement with chiral perturbation theory. Finally, we give results for the distribution functions. We compare our results with Bergknoff's variational study from the infinite momentum frame in the chiral region.

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Section: Discussionmentioning

confidence: 99%

“…Comparison with chiral perturbation theory [16,17]. Fig.5 Dependence of the dimensionless mass of vector and scalar particle on the θ-angle after subtraction of θ-vacuum energy.…”

Section: Discussionmentioning

confidence: 99%

“…Fig.5 Dependence of the dimensionless mass of vector and scalar particle on the θ-angle after subtraction of θ-vacuum energy. Comparison with chiral perturbation theory [16,17]. …”

Section: Discussionmentioning

confidence: 99%

Section: Mass Spectrummentioning

confidence: 99%

See 2 more Smart Citations

The massive Schwinger model - a Hamiltonian lattice study in a fast moving frame

Kröger

Scheu

1998

Physics Letters B

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“…, (24) respectively, wich are found by means of Table 1. Working with color neutral Fock states, all color structure reduces to an overall factor C, with C 2 = (n 2 c − 1)/2n c .…”

Section: The Qq-scattering Amplitudementioning

confidence: 99%

Discretized light-cone quantization and the effective interaction in hadrons

Pauli¹

1999

AIP Conference Proceedings

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Light-cone quantization of gauge theories is discussed from two perspectives: as a calculational tool for representing hadrons as QCD bound-states of relativistic quarks and gluons, and as a novel method for simulating quantum field theory on a computer. A general non-perturbative method for numerically solving quantum field theories, 'discretized light-cone quantization', is outlined. Both the bound-state spectrum and the corresponding relativistic wavefunctions can be obtained by matrix diagonalization and related techniques. Emphasis is put on the construction of the light-cone Fock basis and on how to reduce the many-body problem to an effective Hamiltonian. The usual divergences are avoided by cut-offs and subsequently removed by the renormalization group. For the first time, this programme is carried out within a Hamiltonian approach, from the beginning to the end. Starting with the QCD-Lagrangian, a regularized effective interaction is derived and renormalized, ending up with an almost solvable integral equation. Its eigenvalues yield the mass spectrum of physical mesons, its eigenfunctions yield their wavefunctions including the higher Fock-space components. An approximate but analytic mass formula is derived for all physical mesons.

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Massive Schwinger Model within Mass Perturbation Theory

Adam

1997

Annals of Physics

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In this article we give a detailed discussion of the mass perturbation theory of the massive Schwinger model. After discussing some general features and briefly reviewing the exact solution of the massless case, we compute the vacuum energy density of the massive model and some related quantities. We derive the Feynman rules of mass perturbation theory and discuss the exact n-point functions with the help of the Dyson Schwinger equations. Further, we identify the stable and unstable bound states of the theory and compute some bound-state masses and decay widths. Finally we discuss scattering processes, where the resonances and particle production thresholds of the model are properly taken into account by our methods 1997 Academic Press

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Chiral perturbation theory in the Schwinger model

Cited by 44 publications

References 14 publications

The massive Schwinger model - a Hamiltonian lattice study in a fast moving frame

The massive Schwinger model - a Hamiltonian lattice study in a fast moving frame

Discretized light-cone quantization and the effective interaction in hadrons

Massive Schwinger Model within Mass Perturbation Theory

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