Self-energy and flavor interpretation of staggered fermions

Golterman, Maarten; Smit, Jan

doi:10.1016/0550-3213(84)90424-3

Cited by 242 publications

(351 citation statements)

References 22 publications

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“…[28]). Since we want the transformation laws of pseudoscalar 16 They may still occur in the flavor-diagonal sector, as we will see in the next section.…”

Section: E the Effective Theory And Constraints From Cptmentioning

confidence: 99%

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On the foundations of partially quenched chiral perturbation theory

Bérnard

Golterman

2013

Phys. Rev. D

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It has been widely assumed that partially quenched chiral perturbation theory is the correct lowenergy effective theory for partially quenched QCD. Here we present arguments supporting this assumption. First, we show that, for partially quenched QCD with staggered quarks, a transfer matrix can be constructed. This transfer matrix is not Hermitian, but it is bounded, and it can be used to construct correlation functions in the usual way. Combining these observations with an extension of the Vafa-Witten theorem to the partially quenched theory allows us to argue that the partially quenched theory satisfies the cluster property. By extending Leutwyler's analysis of the unquenched case to the partially quenched theory, we then conclude that the existence and properties of the transfer matrix as well as clustering are sufficient for partially quenched chiral perturbation theory to be the correct low-energy theory for partially quenched QCD.

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“…[28]). Since we want the transformation laws of pseudoscalar 16 They may still occur in the flavor-diagonal sector, as we will see in the next section.…”

Section: E the Effective Theory And Constraints From Cptmentioning

confidence: 99%

“…[24,28] for staggered fermions: 12 9) such that −π/2 < p j , q j ≤ π/2. Operators get relabeled as in 10) etc.…”

Section: Introducing Creation and Annihilation Operatorsmentioning

confidence: 99%

On the foundations of partially quenched chiral perturbation theory

Bérnard

Golterman

2013

Phys. Rev. D

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“…Here the tilde on p indicates the restricted momentum range given by p µ = (n µ − 1/2)(2π/N µ ), n µ = −N µ /4 + 1, · · · , N µ /4. The 4 × 4 real symmetric matrices (Γ µ ) AB come out [30,31] naturally as tensor products of Pauli matrices σ k , and τ k . They commute with 4 × 4 real symmetric flavor matrices Ξ µ which correspond to shift symmetries of the staggered fermion action.…”

Section: Discussionmentioning

confidence: 99%

Fermion production despite fermion number conservation

1995

Self Cite

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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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“…These fermion self-energy corrections have been calculated previously to O (g2) on isotropic lattices for Wilson fermions [ 8,9 ] as well as staggered fermions [ 10 ]. We have extended these calculations to the case of anisotropic lattices [ 5 ].…”

Section: S~(p ) =Sv O(p ) + S(p ) (17)mentioning

confidence: 99%

QCD thermodynamics with light quarks. Quantum corrections to the fermionic anisotropy parameter

Karsch

Stamatescu

1989

Physics Letters B

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We determine the O(g 2) corrections to the anisotropy parameter in the fermionic action, which are required to guarantee a rotational invariant continuum limit on anisotropic lattices. We show the importance of these quantum corrections for QCD thermodynamics on isotropic lattices. Only after including these corrections do we find, on large lattices, agreement between lattice and continuum perturbation theory at finite temperature. The implied renormalization of the operators used in Monte Carlo simulations to measure the energy density leads to a 20% reduction of the fermionic part of the energy density which, to a large extent, compensates the previously found overshooting in the gluonic sector. We reanalyze existing Monte Carlo data for the thermodynamics of QCD with light quarks and extract the entropy density. We find that immediately above the chiral transition the entropy density is already close to the ideal gas value.

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Self-energy and flavor interpretation of staggered fermions

Cited by 242 publications

References 22 publications

On the foundations of partially quenched chiral perturbation theory

On the foundations of partially quenched chiral perturbation theory

Fermion production despite fermion number conservation

QCD thermodynamics with light quarks. Quantum corrections to the fermionic anisotropy parameter

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