Hearts-on Approach to Educational Leadership

Christian educational leaders come equipped with an arsenal of skills, talents, and beliefs rooted in their faith. The synthesis of faith in their daily lives or “hearts-on” approach provides them a solid foundation. Communication is the most important skill for an effective leader. This article provides an overview of the critical elements of communication and their potential impact upon educational leadership. Several communication styles and strategies are discussed and clarified by biblically-inspired directives

Dirac operator index and topology of lattice gauge fields

The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of Neuberger's lattice Dirac operator, is shown to have analogous properties to L\"uscher's geometrical lattice topological charge. The main new result is that it reduces to the continuum topological charge in the classical continuum limit. (This is sketched here; the full proof will be given in a sequel to this paper.) A potential application of the ideas behind fermionic lattice topological charge to deriving a combinatorial construction of the signature invariant of a 4-manifold is also discussed.Comment: 16 pages, based on talk at Chiral'99 (Sept. 13-18, 1999, Taipei), to be published in the Proceeding

Relation between bare lattice coupling and MSbar coupling at one loop with general lattice fermions

A compact general integral formula is derived from which the fermionic contribution to the one-loop coefficient in the perturbative expansion of the MSbar coupling in powers of the bare lattice coupling can be extracted. It is seen to reproduce the known results for unimproved naive, staggered and Wilson fermions, and has advantageous features which facilitate the evaluation in the case of improved lattice fermion formulations. This is illustrated in the case of Wilson clover fermions, and an expression in terms of known lattice integrals is obtained in this case which gives the coefficient to much greater numerical accuracy than in the previous literature.Comment: 26 pages, 1 figure, to appear in Phys.Rev.D. Completely rewritten with new title and new material added (see abstract). Some material from the previous version has been removed since it was superceded by arXiv:0709.078

Axial anomaly and topological charge in lattice gauge theory with Overlap Dirac operator

An explicit, detailed evaluation of the classical continuum limit of the axial anomaly/index density of the overlap Dirac operator is carried out in the infinite volume setting, and in a certain finite volume setting where the continuum limit involves an infinite volume limit. Our approach is based on a novel power series expansion of the overlap Dirac operator. The correct continuum expression is reproduced when the parameter $m_0$ is in the physical region $0<m_0<2$. This is established for a broad range of continuum gauge fields. An analogous result for the fermionic topological charge, given by the index of the overlap Dirac operator, is then established for a class of topologically non-trivial fields in the aforementioned finite volume setting. Problematic issues concerning the index in the infinite volume setting are also discussed.Comment: Latex, 33 pages. v6: shortened and (hopefully) more succinct version, to appear in Ann.Phy

Fermionic topological charge of families of lattice gauge fields

Topological charge of families of lattice gauge fields is defined fermionically via families index theory for the overlap Dirac operator. Certain obstructions to gauge invariance of the overlap chiral fermion determinant, as well as the lattice analogues of certain obstructions to gauge fixings without the Gribov problem, have natural descriptions in this context.Comment: 4p., Lattice2002(chiral) (+ one paragraph not included in the proceedings version for length reasons

Improving the locality of the overlap Dirac operator via approximate solutions of the Ginsparg-Wilson relation

We determine the free field hypercubic Dirac operator which is optimally close to satisfying the Ginsparg-Wilson relation. Inserting this operator into the overlap formula, we show that the analytic locality bound on the resulting overlap Dirac operator is substantially stronger than in the standard case. This improvement generally persists in gauge backgrounds when the plaquette variables are all close to unity.Comment: 3 pages, contributed to Proceedings of Lattice2003(chiral