
	Where results make sense

Topic: Lattice theory

In the News (Sun 27 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Life on the lattice
		The crux of his argument as I understood it was that rooting averages over the four tastes, which have pairwise opposite chiralities, leading to a theory that is not a theory of a single chiral fermion.
		The postulated manifestation of this was an incorrect singular behaviour of the 't Hooft vertex in the rooted theory, which could lead to the wrong physics in singlet channels, particularly the mass of the η'.
		Basically, the partition function for theories of 2d fermions can be reformulated as the partition function for a theory of non-intersecting loops, which can be reformulated as a theory of Ising spins, which then can be simulated efficiently using cluster algorithms.
	latticeqcd.blogspot.com (3055 words)

	Lattice (order) - Wikipedia, the free encyclopedia
		Lattices constitute one of the most prominent representatives of a series of "lattice-like" structures which admit order-theoretic as well as algebraic descriptions, such as semilattices, Heyting algebras, and Boolean algebras.
		The set of compact elements of an arithmetic complete lattice is a lattice with a least element, where the lattice operations are given by restricting the respective operations of the arithmetic lattice.
		These conditions basically amount to saying that there is a functor from the category of sets and functions to the category of lattices and lattice homomorphisms which is left adjoint to the forgetful functor from lattices to their underlying sets.
	en.wikipedia.org /wiki/Lattice_(order) (2282 words)

	Lattice (order) (Site not responding. Last check: 2007-10-19)
		In mathematics, a lattice is a partially ordered set in which all nonempty finite subsets have both a supremum (join) and an infimum (meet).
		On the other hand, lattices can also be characterized as algebraic structures that satisfy certain identities.
		The set of compact elements of an arithmetic (complete) lattice is a lattice with a least element.
	www.sciencedaily.com /encyclopedia/lattice__order_ (2513 words)

	Lattice Gauge Theory & Quantum Chromodynamics: Physics on a 4D Scaffold (Site not responding. Last check: 2007-10-19)
		All these are described by a theory called Quantum Chromodyamics (QCD) in which the quarks and gluons (partons) are endowed with colour charges --- a generalisation of the electric charge in electromagnetism.
		This means that the traditional techniques of perturbation theory, which is used to predict properties of electromagnetic interactions, cannot be generally used in QCD.
		Lattice QCD allows us to extract some information about the non-perturbative aspects of QCD and to predict characteristics of the strong nuclear force.
	www.ph.unimelb.edu.au /~ywong/poster/articles/latqcd2.html (537 words)

	Relativity and Quantum Theory
		However, this theory is inherently a many-body theory with the quanta of the normal modes of the classical field having all the properties of physical particles.
		Likewise, a continuous "chiral symmetry", normally exhibited by a theory of light quarks, is broken by the condensation of chirally oriented quark/anti-quark pairs in the vacuum.
		Lattice QCD calculations are predicting with increasing confidence the temperature of the transition to this new quark-gluon plasma, its equation of state and the latent heat of the transition.
	phys.columbia.edu /~cqft/physics.htm (1637 words)

	The Geometry Junkyard: Geometry of Numbers
		Informally, a lattice is an infinite arrangement of points spaced with sufficient regularity that one can shift any point onto any other point by some symmetry of the arrangement.
		More formally, a lattice can be defined as a discrete subgroup of a finite-dimensional vector space (the subgroup is often required not to lie within any subspace of the vector space, which can be expressed formally by saying that the quotient of the space by the lattice is compact).
		Other types of lattices arise in crystallography and in sphere packing, where they are used to describe the locations of atoms or spheres.
	www.ics.uci.edu /~eppstein/junkyard/lattice.html (669 words)

	1999 Summary of Engineering Research - Physics
		Quantum field theory is the union of quantum mechanics and relativity theory.
		In the theory called quantum chromodynamics, observed particles such as the proton are composed of quarks, held together by forces transmitted by gluons, described by a nonabelian gauge field.
		The study of supersymmetric field theories is of great interest, since it is possible to obtain exact nonperturbative information, which may be of use in understanding the strong coupling regime of realistic field theories.
	www.engr.uiuc.edu /communications/engineering_research/1999/pg000216.htm (599 words)

	Lattice Field Theory
		Quantum field theories of the strong, weak and electromagnetic interaction, namely quantum chromodynamics (QCD), and the Weinberg-Salam model, are generally accepted, while quantum theory of gravity is at best in its infancy.
		The introduction of a space-time lattice is an approximation; to represent reality accurately, the lattice spacing must be small and the overall lattice size large compared to the scale of the problem studied.
		Lattice theorists have made aggressive use of the newest parallel machines and even built specially designed machines, to do their calculations.
	www.nersc.gov /news/greenbook/nersc3/node11.html (1227 words)

	Research Interests (Site not responding. Last check: 2007-10-19)
		Lattice techniques are now in widespread use as tools for nonperturbative studies of quantum field theories.
		The application of similar techniques to the quantization of the gravitational field is, however, hampered by the lack of a consistent lattice formulation of differential geometry, on which the continuum theory of General Relativity rests.
		The ultimate goal of this work is to achieve a consistent lattice theory of gravity which retains a lattice version of the continuum diffeomorphism invariance.
	godel.ph.utexas.edu /Members/timg/vita/resint.html (549 words)

	CERN Courier - Workshop looks through the l - IOP Publishing - article
		However, despite its space-time economy, the lattice approach still needs the power of the world's largest supercomputers to perform all of the calculations that are required to solve the complicated equations describing elementary particle interactions.
		The calculations done using lattice techniques not only provide results that are interesting from a phenomenological point of view, but are also of great importance in the development of our understanding of quantum field theories in general.
		This aspect of lattice field theory was covered by a discussion on lattice chiral symmetry involving L Lellouch of Marseille, T Blum of Brookhaven and F Niedermayer of Bern.
	www.cerncourier.com /main/article/41/4/19 (1249 words)

	Swansea University - Lattice Field Theory
		Lattice Field Theory, Quantum Fields under Extreme Conditions
		The research of the group focuses on the study of QCD using non-perturbative methods based on lattice formulations, typically requiring the use of high performance computers.
		Our particular interests include the hadron spectrum, and the behaviour of QCD under extreme conditions of temperature and/or baryon number density, with applications to physical environments as diverse as the early universe 10-5 seconds after the Big Bang, or the interior of a neutron star.
	www.swan.ac.uk /physics/research/LatticeFieldTheory (173 words)

	CPC Licence Alert (Site not responding. Last check: 2007-10-19)
		The usual hypercubic formulation of lattice gauge theory may be improved by the alternative formulation of the theory of a body- centered hypercubic (BCH) lattice.
		The method for implementing the Monte Carlo algorithm for calculating Wilson loops and lines in an SU(2) gauge theory on a BCH lattice is described.
		SU(2) gauge theory is simulated by importance-sampling Monte Carlo methods on a BCH lattice.
	www.cpc.cs.qub.ac.uk /summaries/AABF.html (254 words)

	TOPCOM, Michael R. Darnel: Theory of Lattice-Ordered Groups; a review of the book and perspective of the literature by ...
		With such a bias in mind, I would not initiate a student in lattice ordered groups and rings with a reading of [LZ71]; it is also too easy to get overwhelmed by the contents, and not easy enough to locate results in it, which makes it problematic as a reference text.
		In any event, the way things stood twenty-odd years ago with monographs in the theory of lattice-ordered groups, for many of the stateside Conrad students [BKW77] was still some years from publication, and when it did appear it came out in French, and then, inexplicably, almost immediately became unavailable from the publisher.
		-groups is the similarity between their role in the theory with that of prime ideals in commutative ring theory.
	at.yorku.ca /t/o/p/c/39.htm (3409 words)

	Sponsorship: Lattice 2005 - XXIII International Symposium on Lattice Field Theory (Site not responding. Last check: 2007-10-19)
		Lattice field theory is a means of probing quantum field theories on the computer.
		Lattice determinations of QCD quantities are combined with experimental measurements to test the Standard Model, our theory of elementary particle physics.
		Lattice QCD is a "Grand Challenge" project requiring large-scale parallel computing resources.
	www.maths.tcd.ie /lat05/sponsor (197 words)

	CPC Licence Alert (Site not responding. Last check: 2007-10-19)
		The Monte Carlo lattice gauge theory algorithm with the metropolis et al.
		The formulation of a gauge theory on a lattice was proposed by Wilson to regulate the divergences of quantum field theory.
		SU(3) gauage theory is simulated on a hypercubical lattice by Monte Carlo methods on a multitasking vector processor, the CRAY X-MP-4.
	www.cpc.cs.qub.ac.uk /summaries/AABT.html (226 words)

	QCD and Lattice Field Theory in a Nutshell
		For a simulation in QCD, the lattice spacing a is taken small compared to the size of a proton, so that discretization effects are small, while the number of lattice points is chosen sufficiently large that the `universe' created this way is larger than the proton size.
		Field theories on a lattice bear a great resemblance to, in fact are identical to, statistical models near criticality.
		The lattice formulation of a field theory therefore benefits greatly from the techniques developed in that area, in particular the Wilson renormalization group.
	www.scsc.ethz.ch /CPP/lft.html (851 words)

	EE 382V: Lattice Theory with Applications (Site not responding. Last check: 2007-10-19)
		They are also useful in other disciplines of mathematics such as combinatorics, number theory and group theory.
		The bias of the course wil be on computational aspects of lattice theory (algorithms) and on applications (esp. distributed systems).
		Lattices: Distributive and Modular Lattices, Lattices as algebraic structures, M3-N5 theorem.
	www.ece.utexas.edu /~garg/f03-lat.html (350 words)

	Citebase - A new fermion Hamiltonian for lattice gauge theory
		Citebase - A new fermion Hamiltonian for lattice gauge theory
		A new fermion Hamiltonian for lattice gauge theory
		Based upon the lattice Dirac operator satisfying the Ginsparg-Wilson relation, we investigate canonical formulation of massless fermion on the spatial lattice.
	citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:hep-lat/0110009 (787 words)

	Life on the lattice
		You can develop effective field theory descriptions in certain limits (Chiral perturbation theory, heavy quark effective theory) but these have low energy bits that must be either fixed by experiments, or matched to a QCD calculation.
		Lattice QCD was invented in the mid-seventies by Kenneth Wilson.
		He was thinking about quantum field theory in general and decided that to understand it better it would be helpful to have a formulation of it that could be put on a computer.
	www.livejournal.com /~manobes (2464 words)

	Quantum Logic and Probability Theory
		Ordered by set-inclusion, the closed subspaces of H form a complete lattice, in which the meet (greatest lower bound) of a set of subspaces is their intersection, while their join (least upper bound) is the closed span of their union.
		Mackey presents a sequence of six axioms, framing a very conservative generalized probability theory, that underwrite the construction of a ‘logic’ of experimental propositions, or, in his terminology, ‘questions’, having the structure of a sigma-orthomodular poset.
		In classical probability theory (and especially in classical statistics) one usually focuses, not on the set of all possible probability weights, but on some designated subset of these (e.g., those belonging to a given family of distributions).
	plato.stanford.edu /entries/qt-quantlog (7961 words)

	Fermilab Lattice Gauge Theory Facility Photos (Site not responding. Last check: 2007-10-19)
		Modern computing hardware used in lattice gauge theory calculations (such as in Fermilab's eighty node cluster shown at right) has a price/performance that is rapidly approaching $1/Megaflop.
		This can be compared with approximately $1,000,000/MF on the VAX 11/780s on which the first numerical lattice calculations were done 20 years ago, and $100/MF for Fermilab's ACPMAPS computer in the early 1990s.
		The next processors installed for lattice work at Fermilab are likely to Pentium 4 duals like the one shown here with 1.4 GHz processors and 800 MHz Rambus memory.
	qcdhome.fnal.gov /photos.html (220 words)

	Representation Theory of Lattice Current Algebras - Yu, Faddeev, Frohlich, Schomerus (ResearchIndex) (Site not responding. Last check: 2007-10-19)
		Abstract: Lattice current algebras were introduced as a regularization of the left- and right moving degrees of freedom in the WZNW model.
		3: Representation theory of Chern Simons observables - Yu, Schomerus
		7 Representation theory of Chern Simons Observables - Yu, Schomerus
	citeseer.ist.psu.edu /alekseev96representation.html (596 words)

	Lattice 2004
		His article on lattice QCD is available on line.
		Lattice 2005 will take place 25-30 July 2005 at Trinity College, Dublin, Ireland.
		LatticeNews is a new mailing list set up to announce future lattice conferences, workshops and other news of interest to lattice field theorists. Message from IAC.
	lqcd.fnal.gov /lattice04 (174 words)

	Citebase - The Savvidy ``ferromagnetic vacuum'' in three-dimensional lattice gauge theory
		The first evidence from lattice simulations is obtained of the existence of a nontrivial minimum in the effective potential.
		We examine in non-Abelian gauge theory the heavy quark limit in the presence of the (anti-)self-dual homogeneous background field and see that a confining potential emerges, consistent with the Wilson criterion, although the potential is quadratic and not linear in the quark separation.
		We investigate SU(2) gauge theory in a constant chromomagnetic field in three dimensions both in the continuum and on the lattice.
	citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:hep-lat/9210028 (1022 words)

	Mini-workshop on New Developments in Lattice Gauge Theory -- Abstracts (Site not responding. Last check: 2007-10-19)
		The role of topological characteristics in the axial anomaly is derived explicitly.
		The challenges for simulations on presently accessible lattices are illustrated both for overlap and domain wall fermions.
		I will describe how these global obstructions, and their index-theoretic interpretations, are reproduced in the Overlap formulation of chiral gauge theory on the lattice.
	www.physics.adelaide.edu.au /cssm/workshops/Mini_Latt_00_Abstracts.html (366 words)

	manobes: Lattice Perturbation Theory
		So we ought to be able to correct for the spacing errors perturbativly, by matching our lattice theory to the continuum theory to some order in perturbation theory.
		The trouble is doing perturbation theory on a lattice is rather hard.
		That is a two loop lattice calculation is roughly as much effort as a three loop continuum one.
	www.livejournal.com /~manobes/28786.html (381 words)

	Lattice Gauge Theory
		The aim of the course is to describe non-perturbative approaches to non-Abelian gauge theories.
		The lattice provides a cutoff for field theory which permits many manipulations beyond the reach of Feynman-diagram perturbation theory.
		After introducing the lattice formulation of QCD, we will develop techniques by using simpler field theories as laboratories: the Ising model, the XY (or planar Heisenberg) model, the Ising gauge theory (due to Wegner), the Abelian gauge theory (related to QED).
	julian.tau.ac.il /~bqs/lgt.html (281 words)

Try your search on: Qwika (all wikis)