David H. Adams

Geometric discretization scheme applied to the Abelian Chern-Simons theory

We give a detailed general description of a recent geometrical discretisation scheme and illustrate, by explicit numerical calculation, the schemes ability to capture topological features. The scheme is applied to the Abelian Chern-Simons theory and leads, after a necessary field doubling, to an expression for the discrete partition function in terms of untwisted Reidemeister torsion and of various triangulation dependent factors. The discrete partition function is evaluated computationally for various triangulations of

A Doubled Discretization of Abelian Chern-Simons Theory

S^3

The semiclassical approximation for the Chern–Simons partition function

and of lens spaces. The results confirm that the discretisation scheme is triangulation independent and coincides with the continuum partition function

Fourth root prescription for dynamical staggered fermions

A new discretization of a doubled, i.e., BF, version of the pure Abelian Chern-Simons theory is presented. It reproduces the continuum expressions for the topological quantities of interest in the theory, namely, the partition function and correlation function of Wilson loops. Similarities with free spinor field theory are discussed, which are of interest in connection with lattice fermion doubling. {copyright} {ital 1997} {ital The American Physical Society}

Accelerated overlap fermions

Abstract The semiclassical approximation for the partition function in Chern–Simons gauge theory is derived using the invariant integration method. Volume and scale factors which were undetermined and had to be fixed by hand in previous derivations are automatically taken account of in this framework. Agreement with Wittens exact expressions for the partition function in the weak coupling (large k) limit is verified for gauge group SU(2) and spacetimes S 3 , S 2 ×S 1 , S1×S1×S1 and L(p,q).

Phase and scaling properties of determinants arising in topological field theories

With the aim of resolving theoretical issues associated with the fourth root prescription for dynamical staggered fermions in lattice QCD simulations, we consider the problem of finding a viable lattice Dirac operator D such that (detD{sub staggered}){sup 1/4}=detD. Working in the flavor field representation we show that in the free field case there is a simple and natural candidate D satisfying this relation, and we show that it has acceptable locality behavior: exponentially local with a localization range vanishing {approx}{radical}(a/m) for lattice spacing a{yields}0. Prospects for the interacting case are also discussed, although we do not solve this case here.

Index of a family of lattice Dirac operators and its relation to the non-Abelian anomaly on the lattice.

Numerical evaluation of the overlap Dirac operator is difficult since it contains the sign function

Rooting issue for a lattice fermion formulation similar to staggered fermions but without taste mixing.

\epsilon(H_w)

Taste symmetry breaking with hypercubic-smeared staggered fermions

of the Hermitian Wilson-Dirac operator

A Note on the Faddeev–Popov Determinant and Chern–Simmons Perturbation Theory

H_w