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# Topic: Twistor

###### In the News (Sat 17 Aug 19)

 Twistor memory - Wikipedia, the free encyclopedia Twistor is a form of computer memory, similar to core memory, formed by wrapping magnetic tape around a current-carrying wire. Twistor is largely the brainchild of a single person, Andrew Bobeck, who later developed bubble memory after generalizing some of the concepts used in Twistor. One major advantage of twistor is that the entire row of twistors enclosed by one of the Y solenoids can be read or written at the same time, because there is no need for a sense/inhibit line. en.wikipedia.org /wiki/Twistor_memory   (825 words)

 Twistor theory - Wikipedia, the free encyclopedia The twistor theory, originally developed by Roger Penrose in 1967, is the mathematical theory which maps the geometric objects of the four dimensional space-time (Minkowski space) into the geometric objects in the 4-dimensional complex space with the metric signature (2,2). The twistor approach appears to be especially natural for solving the equations of motion of massless fields of arbitrary spin. Recently, Edward Witten used twistor theory to understand certain Yang-Mills amplitudes, by relating them to a certain string theory, the topological B model, embedded in twistor space. en.wikipedia.org /wiki/Twistor   (196 words)

 Twistor Theory In Figure 02, while the points A, B, and C in twistor space correspond to lines in space-time, the line P in twistor space corresponds to a point P in space-time - the intersection of the lines A and B. This means that a point in space-time is nonlocal in its deeper nature. A twistor in the PT or PT region has to be represented in the space-time picture by a collection, called a congruence, of null lines that twist around each other in a right-handed or left-handed sense (see Figure 03). Thus, at the quantum level, the twistor space picture suggests that points in space-time lose their distinction and become fuzzy - similar to the uncertainty of the position of an electron in quantum theory, but now it is the very structure in the scaffold being not well-defined. universe-review.ca /R15-19-twistor.htm   (2802 words)

 - Twistor Theory The motivation and one of the initial aims of twistor theory is to provide an adequate formalism for the union of quantum theory and general relativity. Twistors are essentially complex objects, like wavefunctions in quantum mechanics, as well as endowed with holomorphic and algebraic structure sufficient to encode space-time points. In this sense twistor space can be considered more primitive than the space-time itself and indeed provides a background against which space-time could be meaningfully quantised. worldcrossing.com /WebX?230@15.abHldrxGrTp@.1dde6a8f   (234 words)

 About Twistor Twistor is a first novel by John Cramer, who is known to SF readership for his "Alternate View" columns in Analog magazine. "John Cramer's Twistor is a wonderful romp through the several universes of real science, from the thin abstraction of particle theory to the grubby, greasy, problem-plagued experimental laboratory, and on to the intricacies of departmental politics and the pitfalls of institutional funding. Twistor stresses fidelity to science as it is experienced first hand, the primary asset of 'hard' science fiction... faculty.washington.edu /jcramer/Twistor.html   (1274 words)

 No Title   (Site not responding. Last check: 2007-10-08) Recently twistor theory has taken on the guise of mathematics, but originally it was conceived by Roger as a part of physics, relevant to the study of the real world around us. Twistor diagram theory, which aims to recast quantum scattering theory, is perhaps the most ignored aspect of the theory, but nevertheless plays a crucial long-term role. The abstract twistor surfaces are the integral manifolds of the abstract twistor structure. www.math.pitt.edu /~sparling/abbanew/abnew31/abnew31.html   (925 words)

 Twistor Theory Twistors are essentially complex objects and in order to proceed we shall have to consider the complexification of the compactified Minkowski space. The spinor components of a twistor have a natural interpretation in terms of the momentum and angular momentum of a zero rest mass particle. Hence the quantisation rule for twistor theory: dual twistors are represented with derivative operators. users.ox.ac.uk /~tweb/00006/index.shtml   (947 words)

 7.2 The original construction for curved spacetimes ’ of the valence 2 twistor equation (46 The large sphere limit of the 2-surface twistor space and the Penrose construction were investigated by Shaw in the Sommers [344], the Ashtekar-Hansen [23], and the Beig-Schmidt [48] models of spatial infinity in [334, 335, 337]. The twistor equation is solved on the three smooth pieces of the cylinder separately, and the resulting spinor fields are required to be continuous at the edges. www.ii.uj.edu.pl /EMIS/journals/LRG/Articles/lrr-2004-4/articlesu15.html   (2735 words)

 www.myspace.com/twistor TWISTOR was born Matthew Ernest Hogan in the small midwestern college town of Wilmington, Ohio on November 1, 1984. TWISTOR also spins breakbeat, hip-hop, drum'n'bass, and IDM as 'DJ TWISTOR.' The name 'TWISTOR' is based on Sir Roger Penrose's twistor theory. TWISTOR is co-founder (with Miller M. Tinkerhess and Edward H. Waisanen) and Director of A&R at T3Records. www.myspace.com /twistor   (1071 words)

 On the Origins of Twistor Theory Sophus Lie had noted essentially the key "twistor" geometric fact that oriented spheres in complex Euclidean 3-space (including various degenerate cases) could be represented as lines in complex projective 3-space (contact between spheres represented as meeting of lines) already in 1869 (cf. The local isomorphism between the "twistor group" SU(2,2) and the connected component of the group 0(2,4) was explicitly part of the Cartan's (1914) general study and classification of Lie groups. Nevertheless, twistors do not, as yet, provide a new physical theory in the usual sense that predictions -different from those given by conventional procedures are yet forthcoming. users.ox.ac.uk /~tweb/00001/index.shtml   (6439 words)

 Twistor Diagrams TWISTOR theory is the creation of the great British mathematician and physicist, Professor Sir Roger Penrose, FRS, OM. The idea of twistor theory is that space and time should be described in a completely new way using the geometry of twistor space. Technically, this is quite separate from my work in twistor theory, but there is an underlying connection because of my familiarity with Roger Penrose's theory of uncomputability in physics. www.twistordiagrams.org.uk   (423 words)

 [No title] A Twistor is a Pneumo-elastic device that is an inflatable actuator having an axially elongated, flexible, hollow, thin-walled elastic cylindrical shell defining a fluid chamber, Figure 1, [2], [3], [5], [6], [7], and [16]. Two Twistor actuators can be pre-twisted to form the jointed device shown in Figure 2, where the Twistor-pair forms the flextural joint and the bi-directional pneumatic actuator. A Twistor in the untwisted position is said to be at zero degrees. www.me.utexas.edu /~lotario/paynter/hmp/Mechatronic_Joint.html   (1631 words)

 Project IV 05-06 (RSW)   (Site not responding. Last check: 2007-10-08) His underlying idea was to re-formulate theories of physical phenomena (such as gravity) in terms of twistor space rather than space-time: in some sense, the twistor-space description would be more fundamental. Twistor Theory has turned out to have close connections with several areas of mathematics, especially geometry and differential equations. This is the subject of current research, as are the more ambitious aims of twistor theory (such as finding a better approach to quantum field theory). fourier.dur.ac.uk /~dma0rsw/proj.html   (234 words)

 Amazon.co.uk: Twistor: Books   (Site not responding. Last check: 2007-10-08) Soon, because of dirty tricks by industrial spies, David and two small children are trapped in a "shadow" world, an Eden-like twin of the Earth with its own ecology of strange plants and animals, including a peculiarly colorful "tree-bird", a dextrous six-legged "shadow kitten", and a giant tentacle-mouthed "shadow bear". The twistor field is myth, but Cramer creates a curious "new world" feeling, that is imbued with some degree of suspense. Twistor uses the concept of a shadow universe to provide us with a most interesting thriller. www.amazon.co.uk /exec/obidos/ASIN/0380710277   (716 words)

 Twistor theory and graph theory   (Site not responding. Last check: 2007-10-08) Twistor theory is in the overlap between mathematical physics and various branches of mathematics such as algebraic topology and complex differential geometry. For example, Franz Müller (Zürich) and I have published an article on sequential twistor diagrams; we were fortunate to have been invited to the Spaces of geodesics and complex structures in general relativity and differential geometry school, Erwin Schrödinger Institute for Mathematical Physics, Vienna, in Spring 1997. This work is not related to twistor theory, but arose from the study of twistor and spinor diagrams and strand networks, and is joint work with Mike Eastwood (Adelaide). homepage.mac.com /stephen_huggett/research.html   (513 words)

 Proceedings of the American Mathematical Society These are the first examples of twistor spaces of algebraic dimension two over a simply connected Riemannian four-manifold with positive scalar curvature. For this purpose we develop a method to distinguish between twistor spaces of algebraic dimension one and two by looking at the order of a certain point in the Picard group of an elliptic curve. LeBrun, Y.S. Poon: Twistors, Kähler manifolds, and bimeromorphic geometry. www.ams.org /proc/1999-127-09/S0002-9939-99-05406-4/home.html   (444 words)

 Reviews.PDA Live! - PDA Live.com The Pal Pal Twistor is an opaque polycarbonate case that opens in a clam-like fashion. The Pal Pal Twistor looks like a case that would be great for lefties since it opens up clamshell-like, but unfortunately, this isn't quite so. The Pal Pal Twistor is a great idea, but unfortunately there are still some kinks to it that need to be worked out. www.pdalive.com /twistor.php   (898 words)

 SCIENCE OF CONNECTIVENESS 3   (Site not responding. Last check: 2007-10-08) He reasoned that the difficulty may lie in the conventional view of space-time as a smooth, 4-dimensional manifold (which may be curved in the vicinity of gravitational mass). And even though twistors are discrete as opposed to continuous, they can effectively be used to represent space-time, because, at Planck-length dimensions, quantum uncertainty "fuzzes out" a point in twistor space. The twistor concept, therefore, is a symbolic way of representing the on-going creation process of the physical world of space-time via light rays. www.fmbr.org /abstracts/sc3.htm   (9563 words)

 Review: Twistor   (Site not responding. Last check: 2007-10-08) Together with his graduate student Victoria Gordon, who also turns into the target of the inevitable romantic subplot, he accidentally discovers the "twistor" effect, which by way of a weirdly rotating electro-magnetic field opens a gate to parallel "shadow matter" universes predicted by some versions of superstring theory. In the accidental company of a dear friend's two small children, David is forced to flee from the thugs to a shadow universe, destroying the twistor machinery in the process. The twistor effect is well thought-out and in an afterword Cramer draws the line between real science and fictional speculation. sites.inka.de /mips/reviews/Twistor.html   (355 words)

 7.1 Motivations In general the twistor equation has only the trivial solution, but in the (conformal) Minkowski spacetime it has a four complex parameter family of solutions. Thus the quasi-local energy-momentum and self-dual angular momentum of the source are certain spinor parts of the kinematical twistor. However, additional structures, namely the infinity twistor and the Hermitian scalar product, were needed to be able to ‘isolate’ its energy-momentum and angular momentum parts, and, in particular, to define the mass. www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2004-4/articlesu14.html   (673 words)

 AMCA: Twistor and Killing spinors on Lorentzian manifolds and their relations to CR and Kaehler geometry by Helga Baum Twistor spinors were introduced by R. Penrose in General Relativity as solutions j of the conformally covariant twistor equation Parallel and Killing spinors are twistor spinors which satisfy the Dirac equation. The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. at.yorku.ca /c/a/d/q/76.htm   (671 words)

 Collinear | Musings Moreover, it appeared that the known one-loop amplitudes were not easily interpretable in terms of a twistor string theory. Cachazo Svrček and Witten have traced the problem in their earlier analysis to a sort of “holomorphic anomaly.” Their criterion for collinearity in twistor space was that the amplitude should obey a certain differential equation. Their paper is very nice, and seems to show a connection between the off-shell continuation in CSW and the original ways of deriving these amplitudes, using cuts and collinear limits. golem.ph.utexas.edu /~distler/blog/archives/000439.html   (698 words)

 Not Even Wrong » Blog Archive » Oxford Twistor String Conference   (Site not responding. Last check: 2007-10-08) The transparencies from the conference on twistor string theory held two weeks ago at Oxford are now available on-line. As for the motivation and present state of the whole idea of relating QCD to a string theory in twistor space, the only person who really seems to have much to say about this is Witten himself. His transparencies are in three parts: part 1a and part 1b from his first talk and then a second talk in which he explains what the problems with the whole idea are and some ideas he’s been thinking about using to try and get around them. www.math.columbia.edu /~woit/blog/archives/000142.html   (394 words)

 Andrew Hodges - Main Page In 2000 Roger Penrose finally found an approach to the description of gravity in twistor geometry which seems to fit with what I found necessary to develop for the description of quantum field theory. I have started a new website on my twistor work, but please do not expect an explanation in simple terms as this is a bit tricky! Connections betwen twistor theory and string theory now seem to be emerging. www.synth.co.uk /main.html   (957 words)

 Further Advances in Twistor Theory Although twistor theory originated as an approach to the unification of quantum theory and general relativity, twistor correspondences and their generalizations have provided powerful mathematical tools for studying problems in differential geometry, nonlinear equations, and representation theory. Motivated both by questions in differential geometry and by the quest to find a twistor correspondence for general Ricci-flat space times, this volume explores deformed twistor spaces and their applications. Collectively, they trace the development of the twistor programme over the last 20 years and provide an overview of its recent advances and current status. www.ramex.com /title.asp?id=7130   (285 words)

 Page Title Twistor theory is motivated by the idea that the union between space-time structure and quantum-mechanical principles may well involve non-standard quantization procedures. Two guiding principles underlying the twistor approach are holomorphicity (complex analyticity) and non-locality, these seeming to be features that an appropriate "quantized space-time" ought to have. Abstract: Some of these constructions have non-linear versions, and these lead to twistor solutions to the problem of finding anti-self-dual solutions of the Einstein vacuum equations (Ricci-flatness) and the Yang-Mills equations, relevant to strong and weak interactions. www.math.uga.edu /seminars_conferences/penrose.html   (289 words)

 programme.html.doc The Twistor String and Integrability of N=4 SYM Twistor Structure of Loops in N=4 SYM and Higgs + QCD Twistor String Theory and 2T-Physics in d=3, 4, 6, 10 www.maths.ox.ac.uk /~lmason/Tws/programme.html   (77 words)

 Citebase - Massless and Massive Three Dimensional Super Yang-Mills Theory and Mini-Twistor String Theory We adapt the two proposals for twistor string theory, Witten's and Berkovits's, to D=3 super Yang-Mills theory. Recently, Witten proposed a topological string theory in twistor space that is dual to a weakly coupled gauge theory. We construct two matrix models from twistor string theory: one by dimensional reduction onto a rational curve and another one by introducing noncommutative coordinates on the fibres of the supertwistor space P www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:hep-th/0502076   (2046 words)

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