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Topic: Fermion doubling

	Staggered fermion - Wikipedia, the free encyclopedia
		Staggered fermion is a technical subtlety that arises when fermionic fields are included in lattice gauge theory.
		This is known as the fermion doubling problem.
		A particular way to resolve this problem, first proposed by Lenny Susskind and John Kogut, is the staggered fermion approach where a new nonlocal action is constructed where the Dirac operator is treated as a square root.
	en.wikipedia.org /wiki/Staggered_fermion (112 words)

	Sets to Quarks - HyperDiamond Feynman Checkerboard (Site not responding. Last check: 2007-10-25)
		In the HyperDiamond Feynman Checkerboard model, the first generation fermions correspond to octonions O and second generation fermions correspond to pairs of octonions O x O and third generation fermions correspond to triples of octonions O x O x O.
		To calculate the fermion masses in the model, the volume of a compact manifold representing the spinor fermions S8+ is used.
		The Kobayashi-Maskawa parameters are determined in terms of the sum of the masses of the 30 first-generation fermion particles and antiparticles, denoted by Smf1 = 7.508 GeV, and the similar sums for second-generation and third-generation fermions, denoted by Smf2 = 32.94504 GeV and Smf3 = 1,629.2675 GeV.
	www.valdostamuseum.org /hamsmith/Sets2Quarks9.html (6728 words)

	[No title]
		The doubling leads to strong violation of supersymmetry in the limit $N\to\infty$.
		Since there is an exact correspondence between string bits and the algebra of BMN operators even at finite $N$, doubling is expected also on the side of super-Yang--Mills theory.
		We discuss the origin of the doubling in the BMN sector.
	www.thphys.uni-heidelberg.de /cgi-bin/abstracts/hep-th:0302104 (52 words)

	[No title]
		Setting the fermionic action is equivalent to fixing a ``real $K$-cycle'' $(D,\ga,J)$ comprising the generalized Dirac operator, grading and conjugation for the theory.
		In the fermion sector, this form of nonminimal coupling would give rise to a coupling between two fermions and two bosons, which has never been seen.
		Moreover, the fermion doubling demonstrated in \cite{DoubleTrouble} is compounded.
	www.ma.utexas.edu /mp_arc/html/papers/97-52 (4303 words)

	PhD Research Interests
		Their theory, for free lattice fermions, was chirally invariant for a fermion mass of zero, and they claimed that it did not lead to species replication.
		We have modelled interacting fermions with disordered couplings, calculating the logarithm of the ratio of the determinants for the interacting and free case,
		The coupling matrix used was similar to that proposed by L. Jacobs[1] as an implementation of chiral symmetry that didn't lead to fermion doubling,
	www.ph.unimelb.edu.au /~dmartin/random.html (395 words)

	[No title] (Site not responding. Last check: 2007-10-25)
		Instead of projectors onto $L$ or $R$ chirality subspaces, $\gamma ^{5}$ becomes a shift operator in a preferred \emph{% spatial direction.} This interpretation was discovered in an attempt to rectify the problem of four Fermion families in the staggered Fermion approach, and, fortuitously, gives two Fermion ``families,'' even and odd, shifted by the lattice spacing.
		It may be, indeed, that the effect that we obtain a $1+\gamma^5$ chiral interaction with the gauge field in the large scale limit is robust in some larger class of discretizations.
		For example, the NN no-go theorem is an example for robustness of fermion doubling in some class of discretizations.
	ilja-schmelzer.de /GET/EPDVO29comment3.html (798 words)

	Session UC42 - QCD II.
		Another problem in lattice QCD is fermion doubling --- the multiplication of quark species.
		The new fermion formulation, domain wall fermions, decouples the chiral and continuum limits, allowing the full continuum global symmetry group of QCD to be realized at finite lattice spacing.
		Results for QCD at zero and non-zero temperatures, using domain wall fermions and other lattice fermion formulations, will be presented and contrasted, including effects due to internal quark loops.
	flux.aps.org /meetings/YR99/CENT99/abs/S7825.html (622 words)

	4-dim HyperDiamond Lattice
		If fermions live only on the even D4 sublattice, then hep-lat/9508013 by Kevin Cahill in the xxx e-print archive shows that the fermion doubling problem is solved.
		The double cover of (3,3,2) is the 24-element binary tetrahedral group {3,3,2}.
		The /\16 lattice is associated with the octonionic XY-product of Dixon.
	www.valdostamuseum.org /hamsmith/FynCkb.html (6224 words)

	Generalized Pauli-Villars regularization for undoubled lattice fermions (ResearchIndex)
		Abstract: A manifestly gauge invariant formulation of chiral theories with fermions on the lattice is developed.
		The theory is free of fermion doubling, requires only local gauge invariant counterterms and produces correct results when applied to exactly solvable two dimensional models.
		1 Introduction In this paper I discuss a possibility to describe chiral fermions on the lattice in the framework of the...
	citeseer.ist.psu.edu /59318.html (208 words)

	Abstracts for the CSSM Workshop on Lattice QCD
		I present the results of a numerical experiment which shows, against naive expectations, that (i) center vortices are responsible for confinement; (ii) the Abelian monopole condensate disappears when center vortices are removed.
		I report on a calculation of the K to pi matrix elements of the delta S=1 weak Hamiltonian, and on a nonperturbative determination of the strange quark mass.
		We propose a stochastic Monte Carlo algorithm for full QCD in which the fermion determinant is estimated with noise and unbiased subtraction to reduce the variance.
	www.physics.adelaide.edu.au /cssm/workshops/lattice98abstracts.html (726 words)

	PhD Research Interests
		A type of random lattice was investigated in relation to the fermion doubling problem.
		As for the random coupling case, we compared the logarithm of the ratio of interacting and free fermion determinants to the values of naive and Wilson fermions whose properties are well known (fermion doubling and no fermion doubling respectively).
		This behaviour was indeed observed with the results tending towards fermion doubling in the continuum limit.
	www.ph.unimelb.edu.au /~dmartin/deviation.html (217 words)

	[No title] (Site not responding. Last check: 2007-10-25)
		During my recent post doctoral scholarship at the University of Lexington I was working on the implementation of a new noisy algorithm to perform dynamical fermion lattice QCD simulations.
		By incorporating the effects of the fermion determinant the method holds promise as it allows the simulation of an arbitrary number of fermion flavours.
		Although currently still in the design stage, with a substatntial period of time left until the commisioning of the first machine, the architecture brings the promise of a high performance that should allow substantial leaps to be made in the investigation of Lattice QCD.
	www.ph.ed.ac.uk /~bj/UK/CV_Stuff/research_interests.html (975 words)

	Karl Svozil
		The assumptions of the no-go theorem are: a local, homogeneous [translation invariant on the lattice] hermitian hamiltonian, bilinear in the fermion fields; and locally defined, conserved and quantized charges bilinear in the fermion fields [such as the chiral charge].
		Another way out of the dilemma established by the no-go theorem may be the abandonment of [locally defined] point particles and their associated quantum numbers [charges etc.].
		It has been shown, that putting a local fermion field theory on a tesselated space equivalent to its dual lattice, yields well known problems of species doubling.
	tph.tuwien.ac.at /~svozil/publ/catex.htm (1238 words)

	BS: Scientia \| Tangled Bits: Fermions on the Lattice—Part I: The Doubling Problem
		This is a study note based on the book Lattice Gauge Theories, An Introduction, Ch.
		Putting the scalar field on the lattice was pretty stratight forward.
		This is not so for fermions even in the simplest case, i.e.
	www.sfu.ca /~bhosseyn/tangledbits/archives/000387.html (343 words)

	Fundamental Theory Group: Elementary Particles & Fields (Site not responding. Last check: 2007-10-25)
		In the recent past Balachandran and coworkers have made substantial contributions to the theory of quantum field theories on fuzzy spaces.
		They have formulated gauge theories, developed a precise theory of monopoles and instantons, formulated chiral fermions without fermion doubling and proved the axial anomaly in the framework of fuzzy physics.
		Their first study, dealing with abelian theories demonstrated that all spontaneously broken abelian supersymmetric theories admit cosmic string solutions which are superconducting due to fermion zero modes.
	www-hl.syr.edu /depts/physics/FTGElementary.htm (1744 words)

	Honours Projects in Theoretical Physics - 2003
		“Anyons” are a generalization of bosons and fermions, ie under interchange, there is a general phase factor instead of +1 or -1.
		In formulating QCD on a space time lattice, the first step is to construct lattice discretised versions of QCD operators which reproduce the continuum operators as the lattice spacing tends to zero.
		For fermions such as quarks, this has proved to be challenging due to the famous fermion doubling problem.
	www.physics.adelaide.edu.au /new/HonoursProj/CSSMhonours.html (2684 words)

	Webprints
		An unpublished 1974 preprint proposing a solution to the Euclidean fermion doubling problem that overcame a problem with local interactions in an earlier attempt of mine.
		It was rejected by Communications in Mathematical Physics because the referee felt it unlikely that the theory could be renormalizable, due to an extra power of momentum in the Euclidean Dirac two-point function.
		Although I thought it quite possible that the same structure that eliminated the doubling might help the renormalization, I was too depressed at the time to pursue it, and never got around to it again.
	www-personal.umich.edu /~williams/prints.html (463 words)

	U.K. Physics & Astronomy: Graduate Student / PostDoc Seminar
		By discussing the geometry of classical gauge theories, I discuss the formulation of lattice QCD.
		To highlight some of the problems of the lattice I discuss the fermion doubling problem.
		If time permits (and if I write it by Wednesday) I will then discuss what is involved in an actual lattice Monte Carlo calculation, and briefly outline what physical questions may be answered by such computations.
	www.pa.uky.edu /~sarma/GSPD_SEM/GSPD_ABST/abst_balint.html (146 words)

	[No title] (Site not responding. Last check: 2007-10-25)
		We construct the path integral for one-dimensional non-linear sigma models, starting from a given Hamiltonian operator and states in a Hilbert space.
		These rules, which we previously derived in bosonic systems \cite{paper1}, are now extended to fermionic systems.
		We then generalize the work of Alvarez-Gaum\'e and Witten \cite{alwi} by developing a framework to compute anomalies of an $n$-dimensional quantum field theory by evaluating perturbatively a corresponding quantum mechanical path integral.
	celestial.eprints.org /cgi-bin/oaia2/arXiv.org?verb=GetRecord&identifier=oai:arXiv.org:hep-th/9509158&metadataPrefix=oai_dc (115 words)

	[No title] (Site not responding. Last check: 2007-10-25)
		In fact we consider a more general problem, that is, the Dirac operator over an abelian finite group (for which a lattice is a particular example).
		Our results appear to be in direct connexion with the so called fermion doubling problem.
		Quantities like these square-roots have been used recently in order to provide an approach to fermions on the lattice that is free from doubling and has chiral invariance in the massless limit, and our studies seem to give a mathematical basis to it.
	www.clifford.org /anonftp/clf-alg/abstracts/1997/A970726.txt (1427 words)

	Topics: Non-Commutative Field Theory
		Motivation: Non-commutative spaces naturally arise in string theory with a constant background magnetic field in the presence of D-branes; Regularize theories while preserving their symmetries and topological features, and altogether overcoming the fermion-doubling problem.
		Particle physics: A nice result is that, once fermions are fixed, there is no arbitrariness in the Higgs sector.
		@ Fermion fields: Gracia-Bondia et al PLB(98)ht/97, Balachandran et al MPLA(00) [fermion doubling]; Bourouaine and Benslama MPLA(05)ht [Dirac, and gravity], JPA(05) [in em field].
	www.phy.olemiss.edu /~luca/Topics/n/noncomm_ft.html (638 words)

	CDT \| Musings
		Most lattice field theories fall into the former sort, including the Regge-Calculus approach to quantum gravity (in which the edge-lengths of the bonds are the dynamical variables).
		But random lattice models have been proposed as a solution to the Fermion Doubling problem.
		And, of course, they’ve been used in the Dynamical Triangulations approach to quantum gravity, the precursor to CDT.
	golem.ph.utexas.edu /~distler/blog/archives/000713.html (3507 words)

	ph:FT_Numerical
		J. Lawson (Brown), A New Method for Solving Lattice QFT with Dynamical Fermions.
		Currently, I'm doing some work on extending the fermionic methods that Lawson developed.
		A good review of lattice fermions and other issues was given by Kogut:
	www.het.brown.edu /people/hahn/ph/FT_Numerical.html (277 words)

	Avhandlingar från Uppsala universitet : 3930 - Torn, Spun and Chopped (Site not responding. Last check: 2007-10-25)
		Theoretical physics, String theory, D-branes, Non-commutative open string theory, AdS/CFT, Higher spin gauge theory, BMN, String bits, Fermion doubling
		In the second paper we obtain the quadratic scalar field contributions to the stress-energy tensor in the minimal bosonic higher spin gauge theory in four dimensions.
		In the last paper we propose a way to avoid fermion doubling when discretizing the string in the BMN limit.
	publications.uu.se /theses/abstract.xsql?lang=sv&dbid=3930 (483 words)

	Our First Guest Blogger - Lawrence Krauss \| Cosmic Variance
		To a degree, I can understand its ball properties, its magnetic properties, its electrical properties, its molecular properties, its atomic properties, and even its quantum properties, and that’s pretty good, but I still cannot understand its fundamental properties.
		Not sure if you need to vibrate the octonion, it can make a nice fermion representation space just sitting there.
		Baez would like E6/F4 for a spin network but he and Tony Smith agreed it would be tough to do foamy things with it.
	cosmicvariance.com /2005/11/14/our-first-guest-blogger-lawrence-krauss (13617 words)

	fermion doubling problem in deconstruction models
		Deconstruction is the process of replacing the continuous\nfifth dimension with a finite number of points.
		The problem I am having\nis that I encounter fermion doublings for bulk fermion fields as well\nas N=1 chiral multiplets.
		Do you know what I\nshould do?\n\nI HAVE noticed that I can replace bulk fermion fields with two "chains"\nacross the deconstructed points.
	www.physicsforums.com /showthread.php?t=83332 (314 words)

	Luboš Motl's reference frame: Sidneyfest
		But why should we assume that charges and energy-momentum are local?
		This brings to mind the attempts to regularize Weyl fermions on a lattice.
		We encounter fermion doubling problems unless we introduce a nonlocal action.
	www.physics.harvard.edu /QFT/SidneyfestBlog.htm (4012 words)

	Lattice Gauge Theories: An Introduction:9812560629:Rothe, Heinz J.:eCampus.com
		12.2 Hopping Parameter Expansion of the Fermion Propagator in an External Field
		19.5 Temporal Structure of the Fermion Propagator at T not = to 0 and μ not = to 0 in the Continuum
		19.9 Particle-Antiparticle Spectrum of the Fermion Propagator at T not = to 0.
	www.ecampus.com /bk_detail.asp?isbn=9812560629&referrer=CJ (645 words)

	Open Questions in Physics
		Doing so makes heavy use of supercomputers, but there are also fundamental obstacles to good numerical computations, like the "fermion doubling problem", where bright new ideas are needed.
		This was built in 1995, a kilometer underground in the Mozumi mine in Japan.
		This experiment is mainly designed to study neutrinos, but it doubles as a proton decay detector.
	math.ucr.edu /home/baez/open.questions.html (7549 words)

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