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Topic: Compactification (physics)

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	Compactification (physics) - Wikipedia, the free encyclopedia
		In physics, compactification plays an important part in string theory.
		In string theory, compactification refers to "curling up" the extra dimensions (six in the superstring theory), usually on Calabi-Yau spaces or on orbifolds.
		The mechanism behind this type of compactification is described by the Kaluza-Klein theory.
	en.wikipedia.org /wiki/Compactification_(physics) (106 words)

	MATH / PHYSICS Research Group Research
		The analysis and physics of this collision depend entirely on the theory of holomorphic vector bundles and their small instanton phase transitions worked out with Donagi and Pantev.
		Many moduli problems in geometry and physics give rise to setups in which the objects whose variation one wants to study live naturally in a triangulated category rather than in an abelian one.
		Especially important is supersymmetry-breaking physics, which is not well understood in string theory, and which is an essential part of any realistic string model.
	dept.physics.upenn.edu /mprg/resprograms.html (2685 words)

	[No title]
		Given the famous success of mathematical physics in quantitatively describing experimental results, such as the prediction of antimatter by Dirac and the precise agreement between quantum electrodynamics and anomolous magnetic moment of the electron, it is not too crazy to suggest that the universe actually is a mathematical structure.
		Physics is not a finished endevour by any means, but it is not unreasonable to expect that it could be eventually, and thus give a complete discription of the most basic components and laws of reality.
		Physics is generally seen to be the concise, implicit representation of reality - a model - while the "real" reality we all live in is the explicit state of all the quantized interacting fields we are composed of.
	www.physics.unc.edu /~tmgarret/statmeta.tex (6173 words)

	Compactification (physics) Definition / Compactification (physics) Research (Site not responding. Last check: 2007-10-14)
		Physicists study the behavior and properties of matter in a wide variety of contexts, ranging from the sub-microscopic particles from which all ordinary matter is made (particle physics) to the behavior of the material Universe as a whole (cosmology)....
		In string theory, compactification refers to "curling up" the extra dimensions (six in the superstring theory), usually on Calabi-Yau spacesIn mathematics, a Calabi-Yau manifold is a compact Kähler manifold with a vanishing first Chern class.
		The mechanism behind this type of compactification is described by the Kaluza-Klein theoryKaluza-Klein theory (or KK theory, for short) is a model which sought to unify classical gravity and electromagnetism.
	www.elresearch.com /Compactification_(physics) (473 words)

	Superstrings (November 2003) - Physics World - PhysicsWeb
		During the collision or collapse process, all the energy of the initial state goes into forming a single long, tangled string, and the entropy of the configuration is the logarithm of the number of configurations of a random-walking quantum string.
		Even more generally, it should be possible to describe the physics of any region of space in terms of holographic degrees of freedom that reside on the boundary of that region.
		Physically, the smallest compactification value of R is the string scale.
	physicsweb.org /articles/world/16/11/8/2 (2945 words)

	Looking for extra dimensions
		This avoids the situation in the Kaluza-Klein compactification where the Planck mass in four spacetime dimensions depends on the volume of the compactified space, which is hard to control dynamically.
		One problem with theoretical models of gravity and particle physics is that before they can make unique testable predictions of new physics, they have to be worked on so that they don't contradict any existing theoretical or experimental knowledge.
		In superstring theory with Kaluza-Klein compactification, there are several different energy scales that come into play in going from a string theory to a low energy effective particle theory that is consistent with observed particle physics and cosmology.
	superstringtheory.com /experm/exper5a1.html (1201 words)

	The Divinisation Of Matter - Lurianic Kabbalah, Sri Aurobindo, and the New Physics
		However, F.D. Peat simply refers to the contraction of these higher dimensions - the term used in physics is compactification - which then coexist in and as part of our own universe, on a sub-atomic level, and are responsible for the number of families of elementary particles, and the existence of the forces of nature.
		It is interesting to consider the parallels between the quantum physical ten-dimensional theory (assuming of course that these other dimensions are actual dimensions in the same way that the ordinary four dimensions of space-time are) and the "Breaking of the Vessels" of Lurianic Kabbalah.
		This original mathematical "supersymmetry" was broken, resulting in the compactification of six of the original ten space-time dimensions, and a division of the original unity into two universes, our own, and a parallel "shadow universe," and into the four fundamental forces of physical reality we know today.
	www.kheper.net /essays/Divinisation_of_Matter.htm (6699 words)

	Life, the cosmos and everything (October 2001) - Physics World - PhysicsWeb
		The notion that certain features of the universe, such as the values of the physical constants, may be constrained by the requirement that intelligent observers can arise was first mooted nearly 40 years ago.
		The "weak" version accepts the laws of nature and the values of the physical constants as given and claims that the existence of life then imposes a selection effect on where and when we observe the universe.
		This posits that space-time is either 10-dimensional (superstring theory) or 11-dimensional (M-theory), with four-dimensional physics emerging from the compactification of the extra dimensions.
	physicsweb.org /article/world/14/10/3 (3003 words)

	Re: Physics bitten by reverse Alan Sokal hoax?
		As in string theory, beta hat is the > > compactification radius of the theory.
		New answer : In fact, "beta hat" is an inverse function of the dilaton 1/g2, which dilaton being the "compactification radius" of the theory.
		More precisely, in the 5-dimensional metric corresponding to the "extended gravity" at the Planck scale, "the" compactification radius" of the theory is given by the compactification radius r of the fourth timelike direction w of the metric.
	www.lns.cornell.edu /spr/2002-11/msg0046020.html (2187 words)

	``Branification:'' an alternative to compactification
		This raises the exciting prospect that Planckian physics could be observed in high-energy accelerators, provides interesting new techniques to address hierarchy problems in physics, and could possibly lead to novel phenomena in cosmology and fl hole physics.
		The scale at which this ceases to be true, and the underlying infinite fifth dimension is revealed, is set by the anti-de Sitter radius, R.
		The non-compactness of the extra dimension distinguishes these ``branification'' scenarios from compactification, and has novel consequences such as the existence of a continuum of ``Kaluza-Klein'' modes.
	www.phys.lsu.edu /mog/mog15/node11.html (1083 words)

	List of academic publications, delivered talks and lectures
		Kubyshin Yu.A., Mourão J.M., Volobujev I.P. Spontaneous compactification and dimensional reduction.
		Volobujev I.P., Kubyshin Yu.A. Spontaneous compactification from the viewpoint of the dimensional reduction of gauge fields.
		In: "Electroweak Physics and the Early Universe", Proceedings of a NATO Advanced Research Workshop (Sintra, Portugal, 23-25 May, 1994).
	theory.npi.msu.su /~kubyshin/public.html (1617 words)

	Citebase - Algebraic treatment of compactification on noncommutative tori (Site not responding. Last check: 2007-10-14)
		In this paper we study the compactification conditions of the M theory on D-dimensional noncommutative tori.
		In this paper we study generic M(atrix) theory compactifications that are specified by a set of quotient conditions.
		We generalize this to compactification on the noncommutative torus, explain the classification of these backgrounds, and argue that they correspond in supergravity to tori with constant...
	citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:hep-th/9801170 (1049 words)

	Guide to math used in string theory
		After modern mathematics was freed from Euclid's Fifth Axiom by Gauss and Bolyai, Riemann added to modern geometry the abstract notion of a manifold M with points that are labeled by local coordinates that are real numbers, with some metric tensor that determines an extremal length between two points on the manifold.
		Much of the progress in 20th century physics was in applying this modern notion of geometry to spacetime, or to quantum gauge field theory.
		In the quest to develop a notion of quantum geometry, as far back as 1947, people were trying to quantize spacetime so that the coordinates would not be ordinary real numbers, but somehow elevated to quantum operators obeying some nontrivial quantum commutation relations.
	superstringtheory.com /math/math3.html (366 words)

	Looking for extra dimensions
		In superstring theory, Kaluza-Klein compactification has to be done on six space dimensions at once.
		Supersymmetry breaking and compactification of higher dimensions have to work together to give the low energy physics we observe in accelerator detectors.
		Braneworld models in general are very different from superstring Kaluza-Klein compactification models because they don't require there to be so many steps between the Planck scale and the electroweak scale.
	superstringtheory.com /experm/exper51.html (989 words)

	Physics Takes On a Whole New Dimension
		In high-energy physics gravitational effects become important at the Planck scale, which is calculated by combining Planck’s constant, the velocity of light, and the Newtonian gravitational constant.
		There are alternatives to many dimensional spaces with compactification, and this period Science Watch showcases four papers (#2, #3, #5, #7) which propose that the additional spatial dimensions are huge.
		Their paper looks at uncertainties in the nuclear fusion reaction cross sections and comes to the conclusion that experimental errors from the nuclear physics are currently the largest source of error in neutrino predictions.
	www.sciencewatch.com /nov-dec2000/sw_nov-dec2000_page6.htm (979 words)

	Colloquia
		We find that due to the presence of spin-2 Kaluza-Klein states from compactification, a correction to the deflection angle with a strong quadratic dependence on the photon energy is introduced.
		The lack of an observed deviation from the Einstein General Relativity prediction for the deflection angle for photons grazing the Sun in the visible band with 15% accuracy (90% c.l.) implies that the scale M_S has to be larger than 1.4(2/(n-2))^{1/4} TeV and approximately 4 TeV for n=2.
		This lower bound is comparable with that from collider physics constraints.
	www.phys.unsw.edu.au /SCHOOL_INFORMATION/COLLOQUIA/1999/mckellar1.html (152 words)

	Igor Volobuev
		In 1977 received Ph.D. in Physics from the Physics Department of MSU; thesis: "Problems of quantum field theory with momentum space of constant curvature".
		In 1995 received doctor scientiarum from the Physics Department of MSU; thesis: "Physics and geometry of symmetric gauge fields".
		A physical interpretation of the spontaneous compactification solutions in Einstein-Yang-Mills theories was put forward, which is based on the dimensional reduction method of symmetric gauge fields.
	www.machaon.ru /inp50/english/people/Book21-07.htm (507 words)

	Robert Leigh, UIUC Physics (Site not responding. Last check: 2007-10-14)
		Professor Rob Leigh received his bachelor's degree in Theoretical Physics from the University of Guelph in 1986 and his Ph.D. in Theoretical Particle Physics, from the University of Texas at Austin in 1991.
		It provides a framework in which an understanding of the components of the standard model of particle physics may be sought.
		Copyright 2001 by the Department of Physics at the University of Illinois at Urbana-Champaign.
	www.physics.uiuc.edu /People/Faculty/profiles/Leigh (601 words)

	the Bohr compactification of the Reals - Information Technology Services (Site not responding. Last check: 2007-10-14)
		Oh, the bohr cmptfn of the Reals is the dual group of the Reals equipped with a wacko topology called the "discrete" topology in which the real line is totally atomized as if by a giant sneeze and no point is near any other point.
		For that, we define the Bohr compactification B(G) of G as H', where H is as a group G', but given the discrete topology.
		I'm quite out of my depth here, but it occurred to me recently that every prime p could be associated with a sine wave with period p or 1/p and every integer could be represented as a unique wave by taking the sum of the sine waves of it's prime factors.
	www.physicsforums.com /archive/topic/t-14590 (3717 words)

	The Superstring Store
		A collection of early original papers in superstring theory, this volume is instructive in both physics and in the history of physics.
		These are the works that started superstring theory before it was a fully credible enterprise as seen by the larger theoretical physics community.
		A brief introductory description of the new physical and mathematical ideas involved in formulating supersymmetric theories.
	superstringtheory.com /store/advbooks.html (580 words)

	Chang Shih Chan - Thesis on deposit: Department of Physics, Princeton University (Site not responding. Last check: 2007-10-14)
		The thesis of Chang Shih Chan entitled "Aspects of Compactification and Holography in String Theory" has been placed on deposit.
		In this thesis, we explore several aspects of compactification and holography in open and closed string theories.
		We also show how the AdS/CFT correspondence can be applied within the context of warped compactification to give a new perspective on the physics of gravitational collapse.
	pupgg.princeton.edu /www/jh/announcements/THESIS_Chan_Chang.html (324 words)

	Citebase - String thresholds and Renormalisation Group Evolution (Site not responding. Last check: 2007-10-14)
		Using this formalism we show that the radiative contribution to gauge couplings involving only massive Kaluza Klein and winding modes may be calculated to all orders in perturbation theory and determine the full two loop contribution involving light modes and estimate the magnitude of the higher-order contributions.
		A complete 5-dimensional SU(5) unified theory is constructed which, on compactification on the orbifold with two different Z_2's (Z_2 and Z_2'), yields the minimal supersymmetric standard model.
		The physical motivations and the basic construction rules for Type I strings and M-theory compactifications are reviewed in light of the recent developments.
	citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:hep-ph/9908369 (1659 words)

	PhilSci Archive - Definability in Physics
		The concept of definability of physical fields in a set-theoretical foundation is introduced.
		Quantization of the model requires only a null postulate and is then shown to be necessary and sufficient for definability in the theory.
		We obtain scale invariance and compactification of the spatial dimensions effectively.
	philsci-archive.pitt.edu /archive/00002094 (125 words)

	High Energy and Elementary Particles Physics — Science
		To solve the problems arising in the process of deformation quantization the group theoretical instruments and new algebraic methods must be developed.
		Lyakhovsky V.D., Shtykov N.N., The Mass Spectrum in N=11 Supergravitation with SU(3)U(1)/U(1)U(1)-Compactification, Nuclear Physics, 46, N 1, p.p.
		Kulish P.P., Lyakhovsky V.D., Stolin A.A., Chains of Frobenius subalgebras of so(M) and the corresponding twists, Journal of Mathematical Physics, 42, p.p.
	hep.niif.spbu.ru /science/lyakhovsky_e.htm (452 words)

	Fifty Orders of Magnitude Stretch Physics to the Limits
		It is an attempt at a theory of quantum gravity, and it follows an enduring theme of fundamental physics, the unification of the forces.
		Time and again in the history of physics, the intellectual puzzles of diverse phenomena have been solved by a small number of underlying principles and building blocks.
		Strings can be open or closed loops, and the resulting quantum physics depends on the vibrations of strings and their interactions with the topology of the space where they exist.
	www.sciencewatch.com /march-april99/sw_march-april99_page6.htm (941 words)

	Thinking Outside the Box
		True, it is the job, no, the necessity of theorists in physics to take what is known and turn it on its head to discern new knowledge.
		Starting in the early 1920’s, the science of physics was simultaneously reveling in its new foundations and shaking in fear of how tenuous these pillars actually were when they were used together.
		Now, theorists in physics are able to describe a universe where that trick could, in speculation, happen without any mirrors.
	www.physics.pdx.edu /telescope/site9/thinking_outside_the_box.htm (1764 words)

	Theoretical Physics (Site not responding. Last check: 2007-10-14)
		The main area of interest is the derivation of properties of low energy supergravity that may have a bearing on particle physics at accelerator energies from compactifications of heterotic string theories.
		Of these, orbifold compactification, ie compactification on a torus with points identified by a discrete group, is perhaps the best developed.
		In the low energy limit (compared to the string scale) the string theory reduces to an effective N = 1 supergravity theory and it is possible in principle to derive information from the string theory concerning parameters which would otherwise be free parameters of the supergravity theory.
	www.pp.rhul.ac.uk /hep/TEST/research/tp.html (646 words)

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