76,905 research outputs found
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
Book Review: A Change on Our Campuses: Jesuit and Feminist Education: Intersections in Teaching and Learning for the Twenty-First Century, Jocelyn M. Boryczka and Elizabeth A. Petrino, eds.
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 is in the physical
region . 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
Index and overlap construction for staggered fermions
Recent developments regarding index and overlap construction for staggered
fermions are reviewed, highlighting the surprising and unexpected aspects.Comment: proceedings contribution for 28th International Symposium on Lattice
Field Theory, Lattice2010, June 14-19, 2010, Villasimius, Italy (slightly
extended version, 8 pages
Theoretical foundation for the Index Theorem on the lattice with staggered fermions
A way to identify the would-be zero-modes of staggered lattice fermions away
from the continuum limit is presented. Our approach also identifies the
chiralities of these modes, and their index is seen to be determined by gauge
field topology in accordance with the Index Theorem. The key idea is to
consider the spectral flow of a certain hermitian version of the staggered
Dirac operator. The staggered fermion index thus obtained can be used as a new
way to assign the topological charge of lattice gauge fields. In a numerical
study in U(1) backgrounds in 2 dimensions it is found to perform as well as the
Wilson index while being computationally more efficient. It can also be
expressed as the index of an overlap Dirac operator with a new staggered
fermion kernel.Comment: 4 revtex pages. v3: slightly shortened and revised, to appear in
Phys.Rev.Lett
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