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Topic: Gauge group

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Asymptotic freedom

Lagrangian

Erlangen program

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	Gauge theory - Wikipedia, the free encyclopedia
		Gauge theories became even more attractive when it was realized that non-abelian gauge theories reproduced a feature called asymptotic freedom, that was believed to be an important characteristic of strong interactions—thereby motivating the search for a gauge theory of the strong force.
		Note that although gauge theory is dominated by the study of connections (primarily because it's mainly studied by high-energy physicists), the idea of a connection is not essential or central to gauge theory in general.
		One thing to note is that not all gauge transformations can be generated by infinitesimal gauge transformations in general; for example, when the base manifold is a compact manifold without boundary such that the homotopy class of mappings from that manifold to the Lie group is nontrivial.
	en.wikipedia.org /wiki/Gauge_theory (2365 words)

	Gauge theory -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-06)
		Gauge theories are a class of physical theories based on the idea that ((mathematics) an attribute of a shape or relation; exact correspondence of form on opposite sides of a dividing line or plane) symmetry (A qualitative change) transformations can be performed locally as well as globally.
		Gauge theories became even more attractive when it was realized that non-abelian gauge theories reproduced a feature called (Click link for more info and facts about asymptotic freedom) asymptotic freedom, that was believed to be an important characteristic of strong interactions—thereby motivating the search for a gauge theory of the strong force.
		Note that although gauge theory is dominated by the study of (An instrumentality that connects) connections (primarily because it's mainly studied by (Click link for more info and facts about high-energy physicists) high-energy physicists), the idea of a connection is not essential or central to gauge theory in general.
	www.absoluteastronomy.com /encyclopedia/g/ga/gauge_theory.htm (1991 words)

	Gauge theory - Open Encyclopedia (Site not responding. Last check: 2007-10-06)
		Generalizing the gauge invariance of electromagnetism, they attempted to construct a theory based on the action of the (non-abelian) SU(2) symmetry group on the isospin doublet of protons and neutrons, similar to the action of the U(1) group on the spinor fields of quantum electrodynamics.
		There are reps which transform covariantly pointwise (called by physicists gauge transformations of the first kind), reps which transform as a connection form (called by physicists gauge transformations of the second kind) (note that this is an affine rep) and other more general reps, like for example the B field in BF theory.
		If we have a principal bundle whose base space is space or spacetime and structure group is a Lie group, then, the space of smooth (although in physics, we often don't deal with smooth functions) sections of this bundle forms a group, called the group of gauge transformations.
	open-encyclopedia.com /Gauge_theory (1864 words)

	Tissue Coring
		Group 1 received smaller doses of bupivacaine (p < 0.05) and the incidence of arterial hypotension was greater (p < 0.01) and required increased administration of amines (p < 0.01) and perioperative fluid therapy (p < 0.001).
		The incidence of PDPH was 2% in the 0.33 mm group, and 3.5% in the 0.7 mm group.
		The incidence of postdural puncture headache (PDPH) was 4% in the 22-gauge group and 2% in the 25-gauge group.
	www.csen.com /PDPH.htm (14369 words)

	CNGG (Site not responding. Last check: 2007-10-06)
		The Croydon Narrow Gauge Group was formed in December 1981 at a meeting held in the back room of the late Doug Kelly's model railway shop "BRANCH LINE", in the Melbourne suburb of Croydon and the Group has been based in the eastern suburbs of Melbourne, Victoria, Australia ever since.
		The trend by the Group members to build their own self contained layouts is continuing and this means the Group has access to layouts in a number of scale/gauge combinations, which are exhibited by the members under the Group’s banner.
		They are a group of friends who have a common interest in the narrow gauge railways and tramways of the world and who enjoy the companionship of sharing that interest amongst themselves and with the public at exhibitions.
	users.cybernex.net.au /wombat/cngg.htm (1234 words)

	ipedia.com: Gauge theory Article (Site not responding. Last check: 2007-10-06)
		Generalizing the gauge invariance of electromagnetism, they attempted to construct a theory based on the action of the (non-abelian) SU(2) symmetry group on the isospin doublet of protons and neutrons, similar to the action of the U(1) group on the spinor fieldss of quantum electrodynamics.
		Gauge theories became even more attractive when it was realized that non-abelian gauge theories reproduced a feature called asymptotic freedom, that was believed to be an important characteristic of strong interactions - thereby motivating the search for a gauge theory of the strong force.
		In 1983, Simon Donaldson used techniques developed in gauge theory (instantons) to show that the differentiable classification of smooth 4-manifolds is very different from their classification upto homeomorphism, and exhibited exotic differentiable structures on Euclidean 4-dimensional space.
	www.ipedia.com /gauge_theory.html (1563 words)

	5.5 Gauge Group Hom(, R+)
		The gauge group is, therefore, a rather universal object.
		Thus (5.19) shows that the elements of the gauge group are in fact linear transformations and not merely group homomorphisms.
		Finally, let us note that the gauge group is a rather non-typical object from the point of view of classical dimensional analysis.
	www.immt.pwr.wroc.pl /kniga/node22.html (354 words)

	Kent 1985
		Such a gauge group should have dimension at least 4+6+8+10= 28 If U(1)4 is taken to be part of a maximal torus, the rank of the gauge group should be at least 4.
		Electromagnetism has gauge group U(1)4, the maximal torus of Spin(8), but that is reducible to U(l) by considering each of the four U(l)'s in U(l)4 to be one space-time component of the photon in the Feynman path-integral formulation of quantum electrodynamics.
		Spin(8) gauge field theory indicates that there should be three generations of weak bosons, with the second generation having masses around 300 to 400 Gev and the third generation having masses around 18 to 22 Tev, It is from the three generations of weak bosons that Spin(8) gauge field theory gives the Kobayashi-Maskawa parameters.
	www.valdostamuseum.org /hamsmith/Kent.html (2177 words)

	Quantum electrodynamics - Wikipedia, the free encyclopedia
		Mathematically, QED has the structure of an Abelian gauge theory with a U(1) gauge group.
		The gauge field which mediates the interaction between the charged spin-1/2 fields is the electromagnetic field.
		The part of the Lagrangian containing the electromagnetic field tensor describes the free evolution of the electromagnetic field, whereas the Dirac-like equation with the gauge covariant derivative describes the free evolution of the electron and positron fields as well as their interaction with the electromagnetic field.
	en.wikipedia.org /wiki/Quantum_electrodynamics (913 words)

	Directory - Recreation: Models: Railroad: Clubs: United Kingdom
		Gauge 3 Society · cached · The society exists to support the building and running of 2 1/2" (63.5mm) gauge scenic model railways of standard gauge prototypes.
		N Gauge MS Style · cached · A group for people suffering from MS who are interested in N gauge modelling.
		The 7mm Narrow Gauge Association · cached · Organisation of modellers using the scale of 7mm to 1ft.
	www.incywincy.com /default?p=344188 (993 words)

	Loop quantum gravity Article, Loopquantumgravity Information (Site not responding. Last check: 2007-10-06)
		Being closely related to topological quantum field theory and group representationtheory, LQG is mostly established at the level of rigour of mathematical physics, as opposed to string theory, which isestablished at the level of rigour of physics.
		Mathematically LQG is local gauge theory of the self-dual subgroup of the complexified Lorentz group, which is related to the action of the Lorentz group on Weyl spinors commonly used in elementary particle physics.
		Thecompactness of the Lie group avoids some thus-far unsolved difficulties in thequantization of gauge theories of noncompact lie groups, and is responsible for the discreteness of the area and volume spectra.The infamous Immirzi parameter is necessary to resolve anambiguity in the process of complexification.
	www.anoca.org /theory/lqg/loop_quantum_gravity.html (5292 words)

	Cornwall `O`Gauge Group (Site not responding. Last check: 2007-10-06)
		The Cornwall "O" Gauge Group has been in existance for over 25 years, and is affiliated to the Gauge "O" Guild.
		The use of the test track is a regular feature of meeting nights, and in the better weather, at weekends, meetings are held at members homes, who have larger indoor or outside railways.
		Much activity at Cornwall "O" gauge group at their bring and buy evening.
	quicksitebuilder.cnet.com /rmrc/cornwallrailwaymodelerswebsite/id6.html (200 words)

	1st Australian NG Convention - Welcome
		The interest in modelling narrow gauge railways and railroads has been growing over the years, a fact that's very obvious given the ever increasing number of narrow gauge layouts on the exhibition circuit.
		The Croydon Narrow Gauge Group was formed in 1981 and has participated on the exhibition circuit all over Victoria (where we are based) with several trips into South Australia and New South Wales.
		The Croydon Narrow Gauge Group works in two scales: HO (track gauge 9 mm) and O (track gauge 16.5 mm), and uses a modular design that allows inter-changeability of the units.
	www.users.bigpond.com /nawlins/ngc1996/ngc96_w.htm (627 words)

	Symmetry of Einstein-Yang-Mills systems and dimensional reduction
		In this way certain symmetry group G is introduced, and it is tempting to connect this group with internal symmetry groups which are so helpful for classifying of elementary particles multiplets.
		An example of this type of a structure is given by a gauge theory when formulated in terms of fiber bundles.
		For non-Abelian gauge fields one still talks of a non-observable, non-integrable, phase factor [1], but it is no longer connected with representing of quantum mechanical states by rays (1-dimensional subspaces) rather than vectors.
	www.cassiopaea.org /quantum_future/einstein.htm (1330 words)

	East Surrey N-Gauge Group Website
		We are a group of railway modellers working to the N-gauge (9mm track) in a scale of 1:148(British) or 1:160, approximately 2mm to the foot.
		We are a local area group of the National "N" Gauge Society, which publishes a bimonthly journal to over 3000 members.
		Our group currently consists of around 16 members who meet on the third Wednesday of each month in Redhill; our logo is a simplified version of the main lines passing through the junction there.
	www.esng.co.uk /history.htm (371 words)

	E8 (mathematics)
		It is the largest of the five exceptional simple Lie groups.
		This algebra has a 120-dimensional subalgebra generated by as well as 128 new generators that transform as a Weyl-Majorana spinor of.
		This group frequently appears in string theory and supergravity, for example as the U-duality group of supergravity on an eight-torus (a noncompact version), or as a part of the gauge group of the heterotic string (the compact version).
	www.brainyencyclopedia.com /encyclopedia/e/e8/e8__mathematics_.html (177 words)

	icSurreyOnline - Miniature rail fans on track
		More than 200 rail enthusiasts turned out at the sixth N-Gauge Group exhibition which was held in the Methodist Church in Gloucester Road.
		The Reigate station has been created by members of the group and it took centre stage in its full glory at the event.
		The East Surrey N-Gauge Group was formed in 1997 when a number of like-minded enthusiasts were brought together with the intention of sharing their interest in N-Gauge model railways.
	icsurreyonline.icnetwork.co.uk /0100news/0200surreyheadlines/tm_objectid=15442877%26method=full%26siteid=50101%26headline=miniature%2drail%2dfans%2don%2dtrack-name_page.html (245 words)

	Open Directory - Recreation: Models: Railroad: Clubs: United Kingdom (Site not responding. Last check: 2007-10-06)
		Gauge 3 Society - The society exists to support the building and running of 2 1/2" (63.5mm) gauge scenic model railways of standard gauge prototypes.
		The 7mm Narrow Gauge Association - Organization of modelers using the scale of 7mm to 1ft.
		N Gauge MS Style - A group for people suffering from MS who are interested in N gauge modelling.
	dmoz.org /Recreation/Models/Railroad/Clubs/United_Kingdom (1056 words)

	Beliefs-Preferences Gauge Symmetry Group and Replication of Contingent Claims in a General Market Environment
		Beliefs-Preferences Gauge Symmetry Group and Replication of Contingent Claims in a General Market Environment studies the actual financial phenomena underlying the evaluation of financial derivatives, which is today virtually identified with and even replaced by the study of the mathematical aspects of stochastic calculus as a model for such phenomena.
		This volume introduces a fundamental symmetry, a gauge symmetry, between beliefs of market participants and their preferences in a general market environment for a market with exchange of an arbitrary number of arbitrary underlying securities.
		In particular, this beliefs-preferences gauge symmetry makes it possible to obtain an evolution equation that determines, in a general market environment, the values of European contingent claims independent of these beliefs and preferences.
	www.ieslc.com /bpgsg.html (559 words)

	Launceston Model Railway Group (Site not responding. Last check: 2007-10-06)
		Our current exhibition layout is N Gauge, "Lydtor" and is based on Lydford station in Devon.
		Under construction is a replacement N Gauge layout to be based somewhere in the urban North, probably end of steam early diesel era.
		We are at present building a 3mm finescale layout, which is based on the Lake District, and we hope will be finished in time for the 3mm Society 40th anniversary exhibition in 2005.
	quicksitebuilder.cnet.com /rmrc/cornwallrailwaymodelerswebsite/id8.html (130 words)

	Topological Gauge Theories and Group Cohomology - Dijkgraaf, Witten (ResearchIndex)
		Abstract: We show that three dimensional Chern-Simons gauge theories with a compact gauge group G (not necessarily connected or simply connected) can be classified by the integer cohomology group H (BG; Z).
		In a similar way, possible Wess-Zumino interactions of such a group G are classified by H (G; Z).
		The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involves a certain natural map from H (G; Z).
	citeseer.ist.psu.edu /610101.html (669 words)

	Physics Help and Math Help - Physics Forums - Increasing the gauge group in AdS/CFT
		A specific state - some sort of entangled condensate - changes the\nphysics to a physics of a larger gauge group.
		physics to a physics of a larger gauge group.
		We know how to reduce the\nandgt; gauge group by Higgsing - which would happen for a D3-brane - but an\nandgt; anti-D3-brane needs just the opposite.
	www.physicsforums.com /printthread.php?t=41408 (1395 words)

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