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Topic: SU(3)XSU(2)XU(1)

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Gauge theory

Strong nuclear force

W and Z bosons

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Chen Ning Yang

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	[No title] (Site not responding. Last check: 2007-11-05)
		In this paper, the structure of the positive definite Clifford algebra Cl(0,8) of Spin(0,8), and the triality automorphism V8 = S8+ = S8-, are used to reduce the spacetime to 4 dimensions and thereby change the gauge group from Spin(0,8) to the realistic SU(3)xSU(2)xU(1), Higgs, and Gravity.
		The effect of dimensional reduction on fermions, to introduce 3 generations, has been described in hep-ph/9301210.
		The global geometry of manifolds V8 = S8+ = S8- = RP1xS7, the effects of dimensional reduction on them, and the calculation of force strength constants, has been described in hep-th/9302030.
	www.thphys.uni-heidelberg.de /cgi-bin/abstracts/hep-th:9402003 (94 words)

	The Standard Model
		Today, three of the observed forces in Nature have been successfully described as theories of quantum gauge symmetry, and it turns out that these three forces can be described in terms of unitary groups of different dimensions.
		Physicists write this combination of gauge groups as SU(3)xSU(2)xU(1).
		Particle physicists describe this as saying that the symmetry of SU(3)xSU(2)xU(1) is spontaneously broken down to SU(3)xU(1) at the electroweak scale of about 100GeV.
	superstringtheory.com /experm/exper2a.html (760 words)

	Unification and distance scales
		The success of spontaneous symmetry breaking in explaining electroweak physics led physicis to wonder whether the three particle theories of the SU(3)xSU(2)xU(1) model could be the spontaneously broken version of a higher unified theory at some higher energy scale, a single theory with only one gauge group and one coupling constant.
		Because of renormalization, the electromagnetic coupling constant grows larger at high energies, whereas the coupling constants for the weak and strong nuclear interactions grow smaller at higher energies.
		The best candidate for such a theory is unitary group SU(5), which would give 24 gauge bosons mediating the single unified force, but there are also other GUT models based on other groups, such as the orthogonal group SO(10), which would give 45 gauge bosons and contain the SU(5) theory as a subgroup.
	www.superstringtheory.com /experm/exper3a2.html (1002 words)

	Cabi's Glasses: SU(3)xSU(2)xU(1) is special!
		And if you believe in SU(5) unification you are left with a unique choice since only one of the preceding ones can be embedded in the latter.
		Octonions, in particular automorphism group G_2 of octonions, emerge also in super-string model context in intriguing manner as John Baez has explained in his
		Lacking uniqueness (or even having it), it could be interesting first to try to understand the mathematical origin of exceptional superalgebras.
	www.mit.edu /people/cabi/blog/2005/04/su3xsu2xu1-is-special.html (1045 words)

	Proton: stable or unstable? - Page 5
		In the standard model, the 3 lepton families, and the 3 quark families, have a priori not much to do with each other, but the very fact that there are 3 of each cries out for a deeper structure.
		But SU(5) is not equal to SU(3)xSU(2)xU(1), it contains in fac t 24 gauge bosons, so there are EXTRA INTERACTIONS, and some of these link quarks and leptons, which comes down to say that a quark could, through this interaction, change into a lepton.
		Of course one assumes that this symmetry is broken, and that the relevant bosons have a big mass (the "GUT" scale), which decreases this interaction rate.
	www.physicsforums.com /showthread.php?t=15854&page=5 (1904 words)

	Amazon.com: Physical Geometry: Books: Gustavo R. Gonzalez-Martin (Site not responding. Last check: 2007-11-05)
		The quotient of bare masses of three stable particles may be calculated and leads us to a surprising geometric expression, previously known but physically unexplained.
		The combinations of the three fundamental geometric excitations, forming other excitations, may be used to classify particles and show a symmetry under the group SU(3)xSU(2)xU(1).
		A program to establish the relation of the theory with the standard model of particles was outlined...
	amazon.com /Physical-Geometry-Gustavo-R-Gonzalez-Martin/dp/9800767495 (1221 words)

	laws
		In this sense the laws of nature may be be perceived as "random", yet from another angle of perception appear as quite simple.
		It is clear that the fundamental randomness has to be supplemented by certain fundamental assumptions or principles, in order to allow us to derive the observed symmetries, as well as to explain why there are 3+1 dimensions, why we see the symmetry group SU(3)xSU(2)xU(1) at low energy, and why there are three generations.
		The aim of deriving the Standard Model precisely means deriving SU(3)xSU(2)xU(1) with the correct representations, etc, from a few fundamental principles.
	www.nbi.dk /~kleppe/random/law/laws.html (660 words)

	Joe Hucks's Thesis Abstract (Site not responding. Last check: 2007-11-05)
		In Chapter 1, we go through the possible global groups associated with the local SU(3)xSU(2)xU(1) gauge group of the Standard Model.
		There are thirteen possible global groups, of which only nine are compact, and of those nine, only four allow color triplets and weak doublets.
		In Chapter 3, the application of twistor variables to the study of massless spinless particles is reviewed and discussed, and is generalized to give a chiral twistor formalism with first-order Lagrangian for the closed bosonic string in four space-time dimensions.
	www.itp.ucsb.edu /~doug/abs/hucks_phd.html (338 words)

	[ITB] teori kemanunggalan
		Teori gauge SU(3)xSU(2)xU(1) yang biasa disebut sebagai The Standard Model adalah teori yang dimaksud.
		Di dalam teori ini diderivatifkan semua gaya dari transformasi gauge satu grup tunggal -katakanlah- G. Grup kemanunggalan agung ini (haruslah) mengandung grup SU(3)xSU(2)xU(1) sebagai subgrupnya.
		Selain itu grup G ini juga merupakan "simple group" karena ia harus mendiskripsikan gaya terpadu melalui satu konstanta interaksi.
	www.mail-archive.com /itb@itb.ac.id/msg15296.html (682 words)

	Joint Mathematics Colloquium (Site not responding. Last check: 2007-11-05)
		Abstract: Among simple infinite-dimensional Lie super-algebras, one could well be described as "super enlarged SU(3)xSU(2)xU(1)", two odd generators are added to the standard Serre-Chevalley set for SU(3)xSU(2)xU(1).
		This algebra, christened E(3,6) by V. Kac, belongs to the class of simple vector field Lie superalgebras he recently classified.
		It appears that E(3,6) has a remarkable family of complexes of representations too that could be of fundamental importance.
	www.math.neu.edu /bhmn/rudakov.html (93 words)

	Re: Group Theory and Physics
		Because of a profound and amazing theorem in mathematics called Noether's theorem, you can prove that, if a system obeys a symmetry (which can be deduced from group theory once you've found the multiplets (ways of grouping particles)) then there must be a special 'conserved' quantity, like electric charge for example.
		Group theory is so successful (it predicted lots of particles which were found at a later date, predicted quarks, indeed gave rise to most of modern particle physics) that it is now generally believed that the fundamental laws of nature are completely defined by combining a few groups (SU(3)xSU(2)xU(1), in actual fact).
		If (when?) we discover new physics which ISN'T explained by this model, the breakthrough will come from figuring out the new groups.
	www.madsci.org /posts/archives/aug98/901289036.Ph.r.html (441 words)

	Synopsis (Site not responding. Last check: 2007-11-05)
		Here the corresponding internal manifold is already compact.
		(b) The internal symmetry group is SO(d), which provides a natural unification of SU(3)xSU(2)xU(1) for d=10.
		Family replication results if the symmetry group G is slightly larger than Spin(10).
	faculty.physics.tamu.edu /allen/Synopsis.html (643 words)

	Unification and distance
		This type of elementary particle theory is called a Grand Unified Theory or GUT for short.
		The three gauge groups of the Standard Model of known elementary particle physics are SU(3)xSU(2)xU(1).
		In a Grand Unified Theory, these three groups all fit into a single unified group with a unified set of gauge bosons whose number is determined by the properties of the unified group.
	www.superstringtheory.com /experm/exper3.html (1770 words)

	Johns Hopkins University Particle Physics susy
		The cancellation of loop corrections with fermion and boson superpartners tames the heierarchy problem in the Standard Model.
		The presence of low scale SUSY causes the 3 coupling constants of the SU(3)xSU(2)xU(1) Standard Model to unify at large scales.
		The lightest supersymmetric particle is typically stable and could be responsible for the dark matter observed in the universe.
	www.pha.jhu.edu /~morris/jhu_hep/susy.html (333 words)

	Re: What/why these several algebras?
		Yes, most simple Lie groups contain SU(3)xSU(2)xU(1) as a subgroup.
		Of course it's been known for quite a while that SU(3)xSU(2)xU(1) can almost be regarded as a member of the E series of exceptional groups, and so can SU(5) and SO(10).
		So it's perhaps not so surprising that one of the "e" Lie superalgebras is also related to SU(3)xSU(2)xU(1).
	www.lns.cornell.edu /spr/2000-12/msg0030059.html (2931 words)

	Re: What/why these several algebras?
		most Lie groups...) contain >SU(3)xSU(2)xU(1) as a subgroup and their natural >representations look like those of the standard model when >you break the symmetry down to SU(3)xSU(2)xU(1).
		By the way, a small nitpick: SU(5) doesn't contain SU(3)xSU(2)xU(1); it just contains the quotient of this group by Z/6.
		Luckily it's really this quotient group that matters for the Standard Model.
	www.lns.cornell.edu /spr/2000-12/msg0030069.html (1307 words)

	Ch.2 - Event Symmetric Space-Time
		Let us look again at the symmetry we have seen so far.
		There is the SU(3)XSU(2)XU(1) internal gauge symmetry of the of the strong, weak and electromagnetic forces.
		Since these groups are gauged there is actually one copy of the group acting at each event of space-time so the group structure is symbolically raised to the power of the number of points in the space-time manifold
	www.weburbia.com /press/html/g02.htm (7231 words)

	Not Even Wrong » Blog Archive » Model Building
		“… in 1977 … SU(3)xSU(2)xU(1) with the SM particle content was … pretty well set in stone …”.
		in 1974 the 3-2-1 SM was so well accepted that Glashow and Georgi constructed SU(5) GUT based on the fact that SU(5) contains SU(3)xSU(2)xU(1) as a subgroup.
		Although some people in 1977 may have disagreed with the the 3-2-1 3-generation SM, their relevance to physics has been no more significant that the relevance of those who disagree with Einstein’s relativity.
	www.math.columbia.edu /~woit/wordpress/?p=136 (1517 words)

	Main facilities
		The present version has 4 built-in physical models.
		Two of them are the versions of the Standard Model (SU(3)xSU(2)xU(1)) in the unitary and t'Hooft - Feynman gauges.
		The user can change particle interaction and model parameters.
	www-zeuthen.desy.de /~pukhov/COMPHEP/g_infor/node1.html (453 words)

	PC1672: 1.1 Symmetry in physics (Site not responding. Last check: 2007-11-05)
		Einstein's special relativity (which we shall be looking at in more detail)
		the standard model which describes the strong, electromagnetic and weak interactions in particle physics (invariance under SU(3)xSU(2)xU(1) gauge transformations).
		For example, our description of the universe should not depend on our choice of coordinate axes; it should be invariant under rotations.
	theory.ph.man.ac.uk /~mikeb/lecture/pc167/relativity/symmetry.html (451 words)

	Piet Hut: Big Bang: Phase Transitions (Site not responding. Last check: 2007-11-05)
		After the annihilation of the remaining baryons and antibaryons, this slight initial overproduction of baryons may have caused the current dominance of matter over antimatter.
		Starting with some of the early calculations of net baryon number production, we included the extra complications of phase transitions in the vacuum, caused by changes in gauge symmetries necessary to break the original unification into the observed low-energy symmetries of SU(3)xSU(2)xU(1).
		Using a simple model, we made various quantitative estimates for the effect of such phase transitions in our paper
	www.ids.ias.edu /~piet/act/phys/GUT (429 words)

	Voyage vers l'infiniment petit
		Alors pourquoi ne pas essayer de les unifier dans une théorie de jauge où les groupes de symétrie de jauge SU(3)xSU(2)xU(1) se trouvent inclus dans un groupe de symétrie encore plus grand ?
		On peut facilement concevoir dans les Théories de Grande Unification un mécanisme de Higgs qui brise la symétrie SU(5) en SU(3)xSU(2)xU(1), de la même manière que ce même mécanisme, dans le Modèle Standard, brise la symétrie électrofaible SU(2)xU(1) en U(1) de l'électromagnétisme.
		Le groupe SU(5) a 24 générateurs alors que le groupe SU(3)xSU(2)xU(1) n'en a que 12.
	www.diffusion.ens.fr /vip/tableH00.html (1443 words)

	Not Even Wrong » 2005 » September
		Most of the examples he gives of effective theories that may not be low energy limits of a string theory are gauge theories of high rank.
		It’s certainly conceivable that one can argue for something like a bound on the rank of the effective field theory gauge group if it comes from string theory, but there’s absolutely no reason to believe that such an argument can rule out the rank 4 case we care about (SU(3)xSU(2)xU(1)).
		I suppose one can argue that, if say Vafa can show the rank must be less than 500, and the LHC discovers a new gauge theory sector with rank 501, string theory would be falsified.
	www.math.columbia.edu /~woit/wordpress/?m=200509 (2322 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		Availability information may be found in the Availability, Publisher, Research Organization, Resource Relation and/or Author (affiliation information) fields and/or via the "Full-text Availability" link.
		For a journal article, please see the Resource Relation field.
		Transition K/sup 0/..-->..K-bar/sup 0/ in the standard SU(3)xSU(2)xU(1) scheme
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=6491287 (135 words)

	Citebase - Gauge Coupling Running in Minimal SU(3)xSU(2)xU(1) Superstring Unification
		Citebase - Gauge Coupling Running in Minimal SU(3)xSU(2)xU(1) Superstring Unification
		Gauge Coupling Running in Minimal SU(3)xSU(2)xU(1) Superstring Unification
		We study the evolution of the gauge coupling constants in string unification schemes in which the light spectrum below the compactification scale is exactly that of the minimal supersymmetric standard model.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:hep-th/9109053 (199 words)

	Peter Donis Web Site - Math Article 1: Group Theory and Sets (Site not responding. Last check: 2007-11-05)
		The current "standard model" of particle physics, which includes all three of the above forces (i.e., all forces except gravity), is thus based on equations having an SU(3)xSU(2)xU(1) symmetry group structure.
		One line of attack used by physicists who are currently searching for a "Theory of Everything" is to look at still higher-dimensional groups that have SU(3)xSU(2)xU(1) as a subgroup, and therefore might be candidates for the overall symmetry group of everything.
		And now I really am out of breath.
	members.cox.net /peterdonis/math/matharticle1.html (7107 words)

	The Standard Model - Advanced Physics Forums
		Can anyone summarize for me the Standard Model?
		Middling version: SU(3)xSU(2)xU(1) gauge theory with vector bosons (8 SU(3) color-coupled gluons, 3 doublet-coupled SU(2) W\'s, 1 hypercharge-coupled U(1) B).
		The SU(2)xU(1) sector is spontaneously broken by a doublet scalar higgs, making 3 bosons heavy and leaving a massless U(1) photon.
	www.advancedphysics.org /forum/showthread.php?t=293 (570 words)

	INIZIATIVA SPECIFICA FI41
		È in corso di completamento il lavoro sulle osservabili di Dirac del modello standard SU(3)xSU(2)xU(1) delle particelle elementari (L.Lusanna e P.Valtancoli, Dirac's Observables for the SU(3)xSU(2)xU(1) Standard Model).
		[10]L.Lusanna, Dirac's Observables for SU(3)xSU(2)xU(1), invited talk at the
		Colloquium on ``Group Theoretical Methods in Physics", Goslar
	www.fi.infn.it /sezione/rapporti/1996/fi41.html (800 words)

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