Properties of U(1) lattice gauge theory with monopole term

In 4D compact U(1) lattice gauge theory with a monopole term added to the Wilson action we first reveal some properties of a third phase region at negative $\beta$. Then at some larger values of the monopole coupling $\lambda$ by a finite-size analysis we find values of the critical exponent $\nu$ close to, however, different from the Gaussian value.Comment: LATTICE98(higgs

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.Comment: 3 pages, Lattice2004(chiral

Dynamical-parameter algorithm for U(1) gauge theory

We present an algorithm for Monte Carlo simulations which is able to overcome the suppression of transitions between the phases in compact U(1) lattice gauge theory in 4 dimensions.Comment: 6 pages, 2 figures, uuencoded postscript file. Contribution to LATTICE 9

Chiral fermion operators on the lattice

We only require generalized chiral symmetry and $\gamma_5$-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 r\^ole 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.Comment: 25 pages, invited review article for Int. J. Mod. Phys.

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.Comment: 35 pages; v2: Section 9.3 replaced by new Section 10, version to appear in Nucl. Phys.

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 L\"uscher 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.Comment: LATTICE99(chiral fermions), 3 page

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.Comment: 3 pages, Lattice2003(chiral

Phase transition and dynamical-parameter method in U(1) gauge theory

Monte Carlo simulations of the 4-dimensional compact U(1) lattice gauge theory in the neighborhood of the transition point are made difficult by the suppression of tunneling between the phases, which becomes very strong as soon as the volume of the lattice grows to any appreciable size. This problem can be avoided by making the monopole coupling a dynamical variable. In this manner one can circumvent the tunneling barrier by effectively riding on top of the peaks in the energy distribution which meet for sufficiently large monopole coupling. Here we present an efficient method for determining the parameters needed for this procedure, which can thus be implemented at low computational cost also on large lattices. This is particularly important for a reliable determination of the transition point. We demonstrate the working of our method on a 16^4 lattice. We obtain an equidistribution of configurations across the phase transition even for such a relatively large lattice size.Comment: 11 pages, latex, 2 figures included, uuencode