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H. J. Rothe

Publications and source records attributed to H. J. Rothe.

12 recordsLinked to original sources
arXiv2000

Universality of the Axial Anomaly in Lattice QCD

We prove that lattice QCD generates the axial anomaly in the continuum limit under very general conditions on the lattice action, which includes the case of Ginsparg-Wilson fermions. The ingredients going into the proof are gauge invariance, locality of the Dirac operator, absence of fermion doubling, the general form of the lattice Ward identity, and the power counting theorem of Reisz. The results generalize in an obvious way to SU(N) lattice gauge theories.

hep-lat↗
arXiv2000

Chiral symmetry restoration and axial vector renormalization for Wilson fermions

Lattice gauge theories with Wilson fermions break chiral symmetry. In the U(1) axial vector current this manifests itself in the anomaly. On the other hand it is generally expected that the axial vector flavour mixing current is non-anomalous. We give a short, but strict proof of this to all orders of perturbation theory, and show that chiral symmetry restauration implies a unique multiplicative renormalization constant for the current. This constant is determined entirely from an irrelevant operator in the Ward identity. The basic ingredients going into the proof are the lattice Ward identity, charge conjugation symmetry and the power counting theorem. We compute the renormalization constant to one loop order. It is largely independent of the particular lattice realization of the current.

hep-lat↗
arXiv1999

Recursive Construction of Generator for Lagrangian Gauge Symmetries

We obtain, for a subclass of structure functions characterizing a first class Hamiltonian system, recursive relations from which the general form of the local symmetry transformations can be constructed in terms of the independent gauge parameters. We apply this to a non-trivial Hamiltonian system involving two primary constraints, as well as two secondary constraints of the Nambu-Goto type.

hep-th↗
arXiv1999

Renormalization of lattice gauge theories with massless Ginsparg Wilson fermions

Using functional techniques, we prove, to all orders of perturbation theory, that lattice vector gauge theories with Ginsparg Wilson fermions are renormalizable. For two or more massless fermions, they satisfy a flavour mixing axial vector Ward identity. It involves a lattice specific part that is quadratic in the vertex functional and classically irrelevant. We show that it stays irrelevant under renormalization. This means that in the continuum limit the (standard) chiral symmetry becomes restored. In particular, the flavour mixing current does not require renormalization.

hep-lat↗
arXiv1999

Lattice QED and Universality of the Axial Anomaly

We give a perturbative proof that U(1) lattice gauge theories generate the axial anomaly in the continuum limit under very general conditions on the lattice Dirac operator. These conditions are locality, gauge covariance and the absense of species doubling. They hold for Wilson fermions as well as for realizations of the Dirac operator that satisfy the Ginsparg-Wilson relation. The proof is based on the lattice power counting theorem. The results generalize to non-abelian gauge theories.

hep-lat↗
arXiv1999

Master Equation for Lagrangian Gauge Symmetries

Using purely Hamiltonian methods we derive a simple differential equation for the generator of the most general local symmetry transformation of a Lagrangian. The restrictions on the gauge parameters found by earlier approaches are easily reproduced from this equation. We also discuss the connection with the purely Lagrangian approach. The general considerations are applied to the Yang-Mills theory.

hep-th↗
arXiv1999

Hamiltonian Approach to Lagrangian Gauge Symmetries

We reconsider the problem of finding all local symmetries of a Lagrangian. Our approach is completely Hamiltonian without any reference to the associated action. We present a simple algorithm for obtaining the restrictions on the gauge parameters entering in the definition of the generator of gauge transformations.

hep-th↗
arXiv1999

The axial anomaly in lattice QED. A universal point of view

We give a perturbative proof that U(1) lattice gauge theories generate the axial anomaly in the continuum limit under very general conditions on the lattice Dirac operator. These conditions are locality, gauge covariance and the absense of species doubling. They hold for Wilson fermions as well as for realizations of the Dirac operator that satisfy the Ginsparg-Wilson relation. The proof is based on the lattice power counting theorem.

hep-lat↗
arXiv1998

A New Look at the Axial Anomaly in Lattice QED with Wilson Fermions

By carrying out a systematic expansion of Feynman integrals in the lattice spacing, we show that the axial anomaly in the U(1) lattice gauge theory with Wilson fermions, as determined in one-loop order from an irrelevant lattice operator in the Ward identity, must necessarily be identical to that computed from the dimensionally regulated continuum Feynman integrals for the triangle diagrams.

hep-lat↗
arXiv1997

Lattice Artefacts In The Non-Abelian Debye Screening Mass In One Loop Order

We compute the electric screening mass in lattice QCD with Wilson fermions at finite temperature and chemical potential to one-loop order, and show that lattice artefacts arising from a finite lattice spacing result in an enhancement of the screening mass as compared to the continuum. We discuss the magnitude of this enhancement as a function of the temperature and chemical potential for lattices with different number of lattice sites in the temporal direction that can be implemented in lattice simulations. Most of the enhancement is found to be due to the fermion loop contribution.

hep-lat↗