Bound states for overlap and fixed point actions close to the chiral limit

Häusler, Stefan; Lang, C. B.

doi:10.1016/s0370-2693(01)00847-4

Cited by 4 publications

(6 citation statements)

References 39 publications

(49 reference statements)

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“…In massive two-flavour QED 2 the determinant was calculated explicitly to study the masses of the triplet (pion) and singlet (eta) bound states using the overlap and fixed point Dirac operators [5]. Presumably the continuum limit of the determinant itself in the nonperturbative domain discussed below could be used as a sensitive test of the many lattice discretizations of the Dirac operator now in use.…”

Section: Introductionmentioning

confidence: 99%

“…Work in this direction has already begun [3] with the computation of the fermion determinant for massless fermions on a torus using the Neuberger-Dirac operator and the higher-order overlap Dirac operator and the comparison of the results with the exact massless QED 2 determinant on a torus [4]. In massive two-flavour QED 2 the determinant was calculated explicitly to study the masses of the triplet (pion) and singlet (eta) bound states using the overlap and fixed point Dirac operators [5]. Presumably the continuum limit of the determinant itself in the nonperturbative domain discussed below could be used as a sensitive test of the many lattice discretizations of the Dirac operator now in use.…”

Section: Introductionmentioning

confidence: 99%

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Fermion determinant for general background gauge fields

Fry

2003

Phys. Rev. D

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An exact representation of the Euclidean fermion determinant in two dimensions for centrally symmetric, finite-ranged Abelian background fields is derived. Input data are the wave function inside the field's range and the scattering phase shift with their momenta rotated to the positive imaginary axis and fixed at the fermion mass for each partial-wave. The determinant's asymptotic limit for strong coupling and small fermion mass for square-integrable, unidirecitonal magnetic fields is shown to depend only on the chiral anomaly. The concept of duality is extended from one to twovariable fields, thereby relating the two-dimensional Euclidean determinant for a class of background magnetic fields to the pair production probability in four dimensions for a related class of electric pulses. Additionally, the "diamagnetic" bound on the two-dimensional Euclidean determinant is related to the negative sign of ∂ImS eff /∂m 2 in four dimensions in the strong coupling, small mass limit, where S eff is the one-loop effective action.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fermion determinant for general background gauge fields

Fry

2003

Phys. Rev. D

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“…Using bosonization technique [2,3,4,5,6,7,8] the fermionic theory (1) can be mapped onto an equivalent Bose form [2,3,4,5,8,9,10,11,12,13,14,15,16,17,18,19]…”

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confidence: 99%

“…Both the fermionic and the bosonic form of the model has been analyzed by various methods from various aspects, e.g. mass perturbation theory [12], density matrix renormalization group (RG) method [10], lattice calculations [10,14,15], momentum RG method [20], etc. Physical properties (like e.g.…”

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confidence: 99%

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On the renormalization of the bosonized multi-flavor Schwinger model

Nándori

2008

Physics Letters B

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The phase structure of the bosonized multi-flavor Schwinger model is investigated by means of the differential renormalization group (RG) method. In the limit of small fermion mass the linearized RG flow is sufficient to determine the low-energy behavior of the N-flavor model, if it has been rotated by a suitable rotation in the internal space. For large fermion mass, the exact RG flow has been solved numerically. The low-energy behavior of the multi-flavor model is rather different depending on whether N=1 or N>1, where N is the number of flavors. For N>1 the reflection symmetry always suffers breakdown in both the weak and strong coupling regimes, in contrary to the N=1 case, where it remains unbroken in the strong coupling phase.Comment: 13 pages, 2 figures, final version, published in Physics Letters

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Topology and pion correlators — a study in the Nf = 2 Schwinger model

Dürr¹

2002

Nuclear Physics B - Proceedings Supplements

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I readdress the issue whether the topological charge of the gauge background has an influence on a hadronic observable. To this end pion correlators in the Schwinger model with 2 dynamical flavours are determined on subensembles with a fixed topological charge. It turns out that the answer depends on a specific function of the sea-quark mass and the box volume which is in close analogy to the Leutwyler-Smilga parameter in full QCD.

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Bound states for overlap and fixed point actions close to the chiral limit

Cited by 4 publications

References 39 publications

Fermion determinant for general background gauge fields

Fermion determinant for general background gauge fields

On the renormalization of the bosonized multi-flavor Schwinger model

Topology and pion correlators — a study in the Nf = 2 Schwinger model

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