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Topic: Vierbein

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	VANISHING VIERBEIN
		The vanishing of the vierbein is not in general a coordinate-independent statement and what seems to be two points in one coordinate frame could well be seen to be just one in another.
		Vierbein, in the paper, was defined as one-form with values in an associated vector bundle and its vanishing was a coordinate independent statement.
		A zero of a vierbein is accompanied by non-zero torsion.
	quantumfuture.net /quantum_future/papers/vv (1917 words)

	VANISHING VIERBEIN IN GAUGE THEORIES OF GRAVITATION
		We show that a region of space-time with vanishing vierbein but smooth principal connection can be detected by scattering experiments.
		What is new in the paper is connected with this latter question, but I find the discussion misleading and in any case not sufficiently well developed to justify publication in the paper’s present form.
		Although I have shied away from the subject in the intervening years, at the time I was suggesting that "faster-than-light teleportation" is possible but, indeed, I failed to provide the explicit description of a transdimensional remolecularizer working on this principle.
	quantumfuture.net /quantum_future/vanishing_vierbein.htm (323 words)

	[No title]
		The first index is the vierbein index (c ontravariant) and the second one is the coordinate index (covariant).
		The first index is the viervein index (covariant) and the second one is the coordinate index (contrav ariant).
		In this \+ case the number of arguments must be equal to Dimension square." }} {PARA 15 "" 0 "" {TEXT -1 198 "The function vierbein (iveirbein) calcu lates the (inverse) vierbein that are called by omega[-i, j] (omega[i, -j]).
	www.cstp.umkc.edu /public/papers/place/maple/share/Riemann/vierbein.mws (178 words)

	1946-1965 (Site not responding. Last check: 2007-11-06)
		A Kaluza-Klein type unification of the vierbein and electromagnetic fields is developed on the basis of the principal fiber bundle over the four dimensional space-time with the group U(1).
		The vierbein fields and electromagnetic vector potential are unified into the “fünfbein” fields on the bundle space.
		The most general Lagrangian density of the fünfbein fields, which is a function of these fields and of their first derivatives and is quadratic in the derivatives, is given.
	ptp.ipap.jp /link?PTP/67/1946 (384 words)

	General relativity (Site not responding. Last check: 2007-11-06)
		This is an alternative equivalent formulation of general relativity using four reference vector fields, called a vierbein or tetrad.
		One thing to note is that we can perform an independent proper, orthochronous Lorentz transformation at each point (subject to smoothness, of course) and still get a valid tetrad.
		So, the tetrad formulation of GR is a gauge theory, but with a noncompact gauge group SO(3,1).
	www.bidprobe.com /en/wikipedia/g/ge/general_relativity.html (2331 words)

	functions.html
		When the metric or the vierbein is active, the components of the built-in tensors are calculated and simplified automatically.
		The first index is the vierbein index (covariant) and the second one is the coordinate index (contravariant).
		The coordinates and the metric in vierbein and must be given before the vierbein.
	www.astro.queensu.ca /~portugal/ftp/Riemann/functions.html (1300 words)

	Emergent Gravity & Torsion & Dark Energy Metric Engineering
		This Lagrangian is first order in derivatives and is the = = analog for the vierbein formalism of Palatini's Lagrangian.
		This Lagrangian is first order in derivatives and is the = analog for the vierbein formalism of Palatini's Lagrangian.
		This Lagrangian is first order in derivatives and is the analog for the vierbein formalism of Palatini's Lagrangian.
	www.science-one.com /new-5537868-4253.html (3504 words)

	Loop quantum gravity - Wikipedia, the free encyclopedia
		He was able to quantize gravity using gauge field theory.
		In the Ashtekar formulation, the fundamental objects are a rule for parallel transport (technically, a connection) and a coordinate frame (called a vierbein) at each point.
		Because the Ashtekar formulation was background-independent, it was possible to use Wilson loops as the basis for a nonperturbative quantization of gravity.
	en.wikipedia.org /wiki/Loop_quantum_gravity (2033 words)

	Jagd- und Zerstoerergeschwader 23 (Site not responding. Last check: 2007-11-06)
		Born in 1920 Johannes Vierbein had a "good house" family.But his childhood was like hell.Ruined after WWI,Germany just began to ressurect from the ashes.
		He was raised by his mother.His father died in a plane crash in 1920.
		When he was 19,he signed up as a volunteer for Luftwaffe.Johannes hated war,but he loved his country which needed him to help defend Germany.
	www.jzg23.de /dbiovierbein.html (147 words)

	Amazon.de: VHS: 08/15, 1. Teil (Site not responding. Last check: 2007-11-06)
		Asch gilt als einer, der "mit allen Wassern" gewaschen ist, während Vierbein als Niete der Batterie gilt und immer wieder bei Vorgesetzten unangenehm auffällt.
		Während der Gefreite Asch mit allen Wassern gewaschen ist, ist sein Freund Kanonier Vierbein der angebliche Versager und krümmste Hund der Kompanie.
		Vierbein hat aber zweimal 6 Schuß empfangen, da Asch ihm den ersten Ladestreifen bei dem Selbstmordversuch entwendet hat.
	www.amazon.de /exec/obidos/ASIN/B00004RQ6A/imdb-de (1113 words)

	lorentz.html
		Note that if the expansion E is a domain constant, d(E)=0, then all Vierbeins have zero parity, but two of the vierbeins have non-zero topological torsion.
		The same is true for the Vierbein sigma2.
		The vierbeins sigma3 and omega are integrable in all cases.
	www22.pair.com /csdc/maple/lorentz1.html (2550 words)

	Physics Help and Math Help - Physics Forums - Interpretation of GR
		When I first read Rovelli's argument a few weeks ago now, it was a shock to me. Indeed, I remember when I discovered GR through Einstein texts, I felt the orthonormal basis choice was simply ommited in his texts.
		I was of course absolutely anaware at that time that fermions require the vierbein.
		Rovelli had almost convinced me. Wald clearly states that the vierbein formalism is sometime best suited, but that generally speaking, there is no better choice between Einstein's choice, what I refer for convenience here as Rovelli's choice, and Penrose's choice.
	www.physicsforums.com /printthread.php?t=41249 (1932 words)

	Haiko´s Filmlexikon - 08/15 (Site not responding. Last check: 2007-11-06)
		Kasernendrill 1939: Gefreiter Asch und Kanonier Vierbein gehören der gleichen Korporalschaft an.
		Immer häufiger wird Vierbein zu Strafdiensten herangezogen, bis dies schließlich zu seinem körperlichen Zusammenbruch führt.
		Unteroffizier Vierbein wird nach Deutschland kommandiert, um Funkgeräte zu besorgen.
	www.haikosfilmlexikon.de /drama/mn/0815.htm (349 words)

	704-718 (Site not responding. Last check: 2007-11-06)
		New Local Supersymmetry of the Vierbein Formalism and the Dirac Theory
		The new local supersymmetry of the vierbein formalism proposed previously is investigated in detail.
		Gauge fixing and FP-ghost Lagrangian densities are explicitly constructed in a globally super-invariant and BRS-invariant manner.
	ptp.ipap.jp /link?PTP/78/704 (185 words)

	2.5 Proving reflection positivity (Site not responding. Last check: 2007-11-06)
		Furthermore, expanding about flat space, and after appropriate gauge-fixing, they discovered a doubling phenomenon similar to that found for chiral fermions in lattice gauge theory, a behaviour that also persists for different gauge-fixings.
		To ensure the convergence of the functional integration, one has to introduce a damping factor for the vierbeins in the measure, both for Poincaré and conformal gravity [167
		An extension of the results of [167] to supergravity with the super-Poincaré group is also possible [62].
	www.zblmath.fiz-karlsruhe.de /exx/journals/LRG/Articles/lrr-1998-13/node7.html (222 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Thus, once you recognize that you need to consider the action by O(1,3) on Vierbeins seperately from its action on orthogonal bases consisting of (say) two forward pointing null vectors and two spacelike unit vectors, you should be able to see that you can transform between different bases within each class of basis.
		The momentum and energy are only defined wrt Cartesian charts or if you prefer, Vierbeins.
		Different observers (whose world lines are timelike geodesics) will in general measure different momenta and energy for a given object.
	math.ucr.edu /home/baez/PUB/photonframe (520 words)

	Topological Solution with Charge in Gauge Gravity (Site not responding. Last check: 2007-11-06)
		Herein a spherically symmetric solution with charge in the gauge theory of gravity is presented.
		In gauge gravity, the action is taken to be quadratic in the Riemann tensor, and both the vierbein and the spin-connection are considered to be independent dynamical variables.
		Since the spin connection is independent, the theory generally possesses torsion.
	flux.aps.org /meetings/YR00/APR00/abs/S5490009.html (179 words)

	GRONK Downloads (Site not responding. Last check: 2007-11-06)
		All results will be expressed in terms of these functions and their derivatives.
		Vierbeins are only needed for calculating the spin connection and the Dirac operator.
		If you specify a metric and try to calculate these quantities, GRONK will do its best to calculate a vierbein; however, since there is inherently a great deal of arbitrariness in this procedure doing this is not recommended unless absolutely necessary.
	itp.stanford.edu /~zunger/gronk.html (136 words)

	Riemann Package
		One can work with coordinate or with vierbein basis in any dimension.
		In vierbein basis it is necessary to enter the names for the coordinates, the metric in vierbein (generally they are of Lorentz, null or half-null type) and the components of the vierbein.
		The covariant derivative in coordinates basis uses the Christoffel symbols; in vierbein basis it uses the Ricci rotation coefficients.
	www.astro.queensu.ca /~portugal/Riemann.html (432 words)

	HeiDok - Holk, Joachim: Ein neuer Ansatz für den Energie-Impuls-Tensor auf dem Gitter
		In this paper, a novel model for the energy-momentum tensor $\Theta_{\mu\nu}$ of the pure gauge sector on the lattice is developed, motivated by D-dimensional self-similarity considerations regarding space, spacetime, multidimensional thermodynamics, and vierbein calculus within general relativity.
		In contrast to the hitherto introduced lattice models for $\Theta_{\mu\nu}$, the new model presented here is explicitly working with half powers of plaquette variables and can simultaneously fulfil the demands for a uniform construction principle and for a Wilson form of the Hamiltonian component $\Theta_{44}$ as well as for the structure of the trace anomaly.
		The numerical results for the expectation values of the energy-momentum tensor are shown to be sensitive to the construction principle of the underlying model whereas the measurement of the correlators turns out to be dominated by statistical errors.
	www.ub.uni-heidelberg.de /archiv/4070 (489 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Spacetime is taken to have torsion so that the underlying manifold is Riemann-Cartan.
		The vierbein (tetrad) form of the torsion is reduced to a type of $U(1)$ gauge theory and the potential $A_a$ expressed in terms of an order parameter field $\phi^a(x)$.
		When the Jacobian associated with $\phi$ vanishes there are various branchings of the cosmic string.
	www.maths.surrey.ac.uk /personal/st/Mark.Roberts/mrev/mr213.txt (158 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Date: Wed, 29 Dec 2004 19:12:46 GMT (29kb) Date (revised v2): Mon, 17 Jan 2005 16:17:50 GMT (29kb) Title: Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity Authors: Robert Bluhm and Alan Kostelecky Comments: 16 pages REVTeX Report-no: IUHET 478, December 2004 \\ The fate of the Nambu-Goldstone modes arising from spontaneous Lorentz violation is investigated.
		Using the vierbein formalism, it is shown that up to 10 Lorentz and diffeomorphism Nambu-Goldstone modes can appear and that they are contained within the 10 modes of the vierbein associated with gauge degrees of freedom in a Lorentz-invariant theory.
		A general treatment of spontaneous local Lorentz and diffeomorphism violation is given for various spacetimes, and the fate of the Nambu-Goldstone modes is shown to depend on both the spacetime geometry and the dynamics of the tensor field triggering the spontaneous Lorentz violation.
	www.thphys.uni-heidelberg.de /cgi-bin/abstracts/hep-th:0412320 (245 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		They provide a systematic and clear characterization of non-local observables in general relativity with unbroken diffeomorphism invariance, and could yield further differential invariants for four-manifolds.
		The theory includes fluctuations of the vierbein fields, but there exits a non-trivial phase which can be expressed in terms of Witten's topological quantum field theory.
		In this phase, the descent sequences are degenerate, and the corresponding classical solutions can be identified with the conformally self-dual sector of Einstein manifolds.
	celestial.eprints.org /cgi-bin/oaia2/arXiv.org?verb=GetRecord&identifier=oai:arXiv.org:hep-th/9203014&metadataPrefix=oai_dc (135 words)

	Gauge theories with non-unitary parallel transporters: a soluble Higgs model*
		It has been proposed to abandon the requirement that parallel transporters in gauge theories are unitary (or pseudo-orthogonal).
		This leads to a geometric interpretation of Vierbein fields as parts of gauge fields, and non-unitary parallel transport in extra directions yields Higgs fields.
		In such theories, the holonomy group H is larger than the gauge group G.
	www.edpsciences.org /articles/epjc/abs/2005/05/10052_2004_Article_2036/10052_2004_Article_2036.html (240 words)

	Physik: DPG Tagungen 2001 - Sitzung MP 8
		Models of the physical world can be formulated in the theory of complex systems as networks of binary relations (links) between objects or agents.
		This elucidates the question in what way complex systems are generalizations of gauge theories.
		It is possible to discriminate between links which are generalizations of gauge fields, of vierbein fields, and of Higgs fields.
	www.dpg-tagungen.de /archive/2001/html/mp_8.html (275 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		The reduced phase space variables are the holonomies of a flat connection for loops which form a basis of the first homotopy group, and elements of the second cohomology group with value in the Lie algebra L(G).
		When G=SO(3,1), and if the two-form can be expressed as B= e ^ e$, for some vierbein field e, then the variables represent a flat spacetime.
		This is not always possible: We show that the solutions of the theory generally represent spacetimes with ``global torsion''.
	www.nuclecu.unam.mx /~fengari/CMP1.html (149 words)

	05 Einbein, Zweibein, Dreibein, Vierbein
		Da kommt ein Vierbein und nimmt dem Zweibein das Einbein weg.
		Da kommt ein Hund (Vierbein) und nimmt dem Mensch (Zweibein) das Hühnerbein (Einbein) weg.
		Da nimmt der Mensch (das Zweibein) den Hocker (Dreibein) und schlägt den Hund (Vierbein).
	www.uni-erfurt.de /kommunikationswissenschaft/forschungsprojekte/WaKo3D_Web/Texte/05_Verarbeiten/Uebung/einbein.htm (159 words)

	Loop quantum gravity -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		He was able to quantize gravity using (Click link for more info and facts about gauge field theory) gauge field theory.
		In the Ashtekar formulation, the fundamental objects are a rule for (Click link for more info and facts about parallel transport) parallel transport (technically, a (An instrumentality that connects) connection) and a coordinate frame (called a (Click link for more info and facts about vierbein) vierbein) at each point.
		Because the Ashtekar formulation was background-independent, it was possible to use (Click link for more info and facts about Wilson loop) Wilson loops as the basis for a nonperturbative quantization of gravity.
	www.absoluteastronomy.com /encyclopedia/l/lo/loop_quantum_gravity.htm (7526 words)

	CERN Courier - Framing Lorentz symmetry - IOP Publishing - article
		Kostelecky presented some of the myriad of features of the SME in a curved space-time.
		Particles with spin are incorporated into the space-time structure using the "vierbein" formalism, rather like a mathematical four-legged spider placed in a smoothly varying manner at each point in the manifold.
		The coefficients for Lorentz violation acquire additional dependence on features such as the space-time metric and on associated properties like torsion and curvature.
	www.cerncourier.com /main/article/44/10/18 (1750 words)

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