Susskind fermions on a euclidean lattice

Sharatchandra, H. S.; Thun, H.J.; Weisz, Peter

doi:10.1016/0550-3213(81)90200-5

Cited by 292 publications

(240 citation statements)

References 11 publications

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“…This leads to the two time-slice construction described in refs. [24,30,32], where we interpret the χ fields at odd time slices as 'type a' and at even time slices as 'type a + ', writing…”

Section: Discussionmentioning

confidence: 99%

“…In the infinite volume limit the energy density E 0 /N approaches a smooth function of A, In this appendix we construct the transfer operator for vector QED 2 and rederive from it the energy spectrum. To the path integral a quantum mechanical Hilbert space is associated according to the coherent state formalism [24,33]. A rudimentary set of formulas for this purpose is given by…”

Section: Discussionmentioning

confidence: 99%

“…It has been shown in ref. [24] that the natural choice for the axial current in the gauge invariant vector QED 2 , for example, has the expected anomalous divergence equation; see [25] for U(4) × U(4) currents in staggered fermion QCD.…”

Section: Axial and Vector Qed In The Continuummentioning

confidence: 99%

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Fermion production despite fermion number conservation

1995

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Lattice proposals for a nonperturbative formulation of the Standard Model easily lead to a global U(1) symmetry corresponding to exactly conserved fermion number. The absence of an anomaly in the fermion current would then appear to inhibit anomalous processes, such as electroweak baryogenesis in the early universe. One way to circumvent this problem is to formulate the theory such that this U(1) symmetry is explicitly broken. However we argue that in the framework of spectral flow, fermion creation and annihilation still in fact occurs, despite the exact fermion number conservation. The crucial observation is that fermions are excitations relative to the vacuum, at the surface of the Dirac sea. The exact global U(1) symmetry prohibits a state from changing its fermion number during time evolution, however nothing prevents the fermionic ground state from doing so. We illustrate our reasoning with a model in two dimensions which has axial-vector couplings, first using a sharp momentum cutoff, then using the lattice regulator with staggered fermions. The difference in fermion number between the time evolved state and the ground state is indeed in agreement with the anomaly. A study of the vacuum energy shows that the perturbative counterterm needed for restoration of gauge invariance is insufficient in a nonperturbative setting. For reference we also study a closely related model with vector couplings, the Schwinger model, and we examine the emergence of the θ-vacuum structure of both theories.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Fermion production despite fermion number conservation

1995

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“…With the demise of the Wilson-Yukawa approach, this past year has also seen renewed interest in the staggered fermion [40,41,42] approach toward constructing a lattice standard model [18,33,43]. For details of the method, see [33,44].…”

Section: Staggered Fermion Approachmentioning

confidence: 99%

Chiral gauge theories and fermion-Higgs systems

Petcher

1993

Nuclear Physics B - Proceedings Supplements

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“…Another popular approximation [3,4] arises from the simplicity of the staggered fermion formulation [5,6,7]. With only one Dirac component on each site, the large matrix inversions required are substantially faster than with other fermion formulations.…”

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confidence: 99%

Chiral anomalies and rooted staggered fermions

Creutz

2007

Physics Letters B

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A popular approximation in lattice gauge theory is an extrapolation in the number of fermion species away from the four fold degeneracy natural with the staggered fermion formulation. I show that the procedure mutilates the expected continuum holomorphic behavior in the quark masses. This is due to a chiral symmetry group that is of a higher rank than desired. The conventional resolution proposes canceling the unphysical singularities with a plethora of extra states appearing at finite lattice spacing. This unproven conjecture requires an explicit loss of unitarity and locality. Even if correct, the approach implies large cutoff effects in the low-energy flavor-neutral sector.

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Susskind fermions on a euclidean lattice

Cited by 292 publications

References 11 publications

Fermion production despite fermion number conservation

Fermion production despite fermion number conservation

Chiral gauge theories and fermion-Higgs systems

Chiral anomalies and rooted staggered fermions

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