Searcharxiv⌕ Search

arXiv subjects

Werner Kerler

Publications and source records attributed to Werner Kerler.

At least 19 recordsLinked to original sources
arXiv2010

Ergodic SO(3), monopole condensation and vortex free energy

We study the continuum limit of adjoint SU(2) LGT by means of a suppression term for Z2 monopoles. High barriers for tunnelling among different twist sectors are overcome through parallel tempering. Monopole condensation is used to study the deconfinement transition and the properties of the confined phase. Ergodicity in summing over all twist sectors allows an unbiased measure of the 't Hooft vortices free energy. Its behaviour in the SO(3) confined phase hints at differences from what conjectured for semi-integer discretizations.

hep-lat↗
arXiv2005

Gauge transformations in non-perturbative chiral gauge theories

We reconsider gauge-transformation properties in chiral gauge theories on the lattice observing all pertinent information and show that these properties are actually determined in a general way for any gauge group and for any value of the index. In our investigations we also clarify several related issues.

hep-lat↗
arXiv2004

Lattice formulation of chiral gauge theories

We present a general formulation of chiral gauge theories, which admits Dirac operators with more general spectra, reveals considerably more possibilities for the structure of the chiral projections, and nevertheless allows appropriate realizations. In our analyses we use two forms of the correlation functions which both also apply in the presence of zero modes and for any value of the index. To account properly for the conditions on the bases the concept of equivalence classes of pairs of them is introduced. The behaviors under gauge transformations and under CP transformations are unambiguously derived.

hep-lat↗
arXiv2004

Formulation of chiral gauge theories

We present a formulation of chiral gauge theories, which admits more general spectra of Dirac operators and reveals considerably more possibilities for the structure of the chiral projections. Our two forms of correlation functions both also apply in the presence of zero modes and for any value of the index. The decomposition of the total set of pairs of bases into equivalence classes is carefully analyzed. Transformation properties are derived.

hep-lat↗
arXiv2003

General chiral gauge theories on the lattice

We still extend the large class of Dirac operators decribing massless fermions on the lattice found recently, only requiring that such operators decompose into Weyl operators. After deriving general relations and constructions of operators, we study the basis representations of the chiral projections. We then investigate correlation functions of Weyl fermions for any value of the index, stressing the related conditions for basis transformations and their consequences, and getting the precise behaviors under gauge transformations and CP transformations. Various further developments include considerations of the explicit form of the effective action and of a representation of the general correlation functions in terms of alternating multilinear forms. For comparison we also consider gauge-field variations and their respective applications. Finally we compare with continuum perturbation theory.

hep-lat↗
arXiv2003

General chiral gauge theories

Only requiring that Dirac operators decribing massless fermions on the lattice decompose into Weyl operators we arrive at a large class of them. After deriving general relations from spectral representations we study correlation functions of Weyl fermions for any value of the index, stressing the related conditions for basis transformations and getting the precise behaviors under gauge and CP transformations. Using the detailed structure of the chiral projections we also obtain a form of the correlation functions with a determinant in the general case.

hep-lat↗
arXiv2002

Chiral fermion operators on the lattice

We only require generalized chiral symmetry and $γ_5$-hermiticity, which leads to a large class of Dirac operators describing massless fermions on the lattice, and use this framework to give an overview of developments in this field. Spectral representations turn out to be a powerful tool for obtaining detailed properties of the operators and a general construction of them. A basic unitary operator is seen to play a central rôle in this context. We discuss a number of special cases of the operators and elaborate on various aspects of index relations. We also show that our weaker conditions lead still properly to Weyl fermions and to chiral gauge theories.

hep-lat↗
arXiv2002

More chiral lattice fermions

Instead of the Ginsparg-Wilson relation only generalized chiral symmetry is required. The resulting much larger class of Dirac operators for massless fermions is investigated and a general construction for them is given. It is also shown that the new class still leads properly to Weyl fermions and to chiral gauge theories.

hep-lat↗
arXiv2002

More chiral operators on the lattice

Instead of the Ginsparg-Wilson (GW) relation we only require generalized chiral symmetry and show that this results in a larger class of Dirac operators describing massless fermions, which in addition to GW fermions and to the ones proposed by Fujikawa includes many more general ones. The index turns out to depend solely on a basic unitary operator. We use spectral representations to analyze the new class and to obtain detailed properties. We also show that our weaker conditions still lead properly to Weyl fermions and to chiral gauge theories.

hep-lat↗
arXiv2002

Form and index of Ginsparg-Wilson fermions

We clarify the questions rised by a recent example of a lattice Dirac operator found by Chiu. We show that this operator belongs to a class based on the Cayley transformation and that this class on the finite lattice generally does not admit a nonvanishing index, while in the continuum limit, due to operator properties in Hilbert space, this defect is no longer there. Analogous observations are made for the chiral anomaly. We also elaborate on various aspects of the underlying sum rule for the index.

hep-lat↗
arXiv2001

General Ginsparg-Wilson fermions and index

We show rigorously that for general Ginsparg-Wilson fermions the dimensions of the geometric eigenspace and of the algebraic one for zero modes agree so that the index theorem on the lattice is not spoiled by unwanted additional terms.

hep-lat↗
arXiv2001

Chiral fermions on the lattice and index relations

Comparing recent lattice results on chiral fermions and old continuum results for the index puzzling questions arise. To clarify this issue we start with a critical reconsideration of the results on finite lattices. We then work out various aspects of the continuum limit. After determining bounds and norm convergences we obtain the limit of the anomaly term. Collecting our results the index relation of the quantized theory gets established. We then compare in detail with the Atiyah-Singer theorem. Finally we analyze conventional continuum approaches.

hep-lat↗
arXiv1999

Dirac operator normality and chiral fermions

Normality of the Dirac operator is shown to be necessary for chiral properties. From the global chiral Ward identity, which in the continuum limit gives the index theorem, a sum rule results which constrains the spectrum. The Ginsparg-Wilson relation is to be restricted to its simple form and is a member of a set of spectral constraints. A family of alternative chiral transformations is introduced. The one of Lüscher is a special case which transports only the anomaly term to the measure. An alternative transformation would also be needed to correct Fujikawa's path-integral approach. From a general function of the hermitean Wilson-Dirac operator the one of Neuberger follows.

hep-lat↗
arXiv1999

Dirac operator normality and chiral properties

Normality and $\ga$-hermiticity are what gives rise to chiral properties and rules. The Ginsparg-Wilson (GW) relation is only one of the possible spectral constraints. The sum rule for chiral differences of real modes has important consequences. The alternative transformation of Lüscher gives the same Ward identity as the usual chiral one (if zero modes are properly treated). Imposing normality on a general function of the hermitean Wilson-Dirac operator $H$ leads at the same time to the GW relation and to the Neuberger operator.

hep-lat↗