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Topic: Majorana spinor

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Ettore Majorana

Majorana spinor

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	Bloom on Susy
		The susy geometry is an extension in spinor and spinor* directions, which are curved over spacetime, such that parralelograms do not close unless you also shift in spacetime.
		A 32-component spinor means the (N=1) susy must have 32 supercharges (susy is parameterized by a spinor).
		Now, the dimension of spinors cuts down to 4, but the number of supercharges must be the same.
	www.cbloom.com /physics/susy.html (2398 words)

	Spinor: Viele Informationen uber Spinor an omega.it
		Ein Spinor ist in der Mathematik, und dort speziell in der Differentialgeometrie, ein Vektor in einer kleinsten Darstellung (ρ,V) einer Spin-Gruppe.
		Die Spin-Gruppe ist isomorph zu einer Teilmenge einer Clifford-Algebra, jede Clifford-Algebra ist isomorph zu einer Teil-Algebra einer reellen, komplexen oder quaternionischen Matrix-Algebra.
		Die Majorana-Spinor-Darstellung, nach Ettore Majorana, sowohl der Spin-Gruppe als auch der Clifford-Algebra ist die kleinste reelle Darstellung von Cℓ(1,3).
	www.omega.it /s/sp/spinor.html (591 words)

	Kids.Net.Au - Encyclopedia > Spinor
		Spinors are certain kinds of mathematical objects similar to vectors, but which change sign under a rotation of 360 degrees.
		Spinors were invented by Wolfgang Pauli and Paul Dirac to describe the physical property of spin.
		The most typical type of spinor, the Dirac spinor, is a member of the fundamental representation of the complexified Clifford algebra C(p,q), into which Spin(p,q) may be embedded.
	www.kids.net.au /encyclopedia-wiki/sp/Spinor (297 words)

	NationMaster - Encyclopedia: Spinor
		A spinor is a representation of the double cover of the rotation group SO(n,R), or more generally the generalized special orthogonal group, SO(p,q,R), where p+q=n for spinors in a space with a nontrivial metric signature, which is a real Lie group called the spinor group Spin(p,q), which is odd under a rotation by 2π.
		Spinors are sometimes described as "square roots of vectors" because the vector representation sometimes appears in the tensor product of two copies of the spinor representation.
		Spinors provide a means to represent rotations in 'n' dimensions, a spinor turns into a negative when it does a complete rotation.
	www.nationmaster.com /encyclopedia/Spinor (3036 words)

	Spinor - ExampleProblems.com
		In mathematics and physics, in particular in the theory of the orthogonal groups, spinors (pronounced ['spɪnɚs], but the i sound is as in Linux) are certain kinds of mathematical objects (group representations of Spin(n), roughly speaking) similar to vectors, but which change sign under a rotation of 2π radians.
		A spinor of a certain type is an element of a specific projective representation of the rotation group SO(n,R), or more generally of the group SO(p,q,R), where p + q = n for spinors in a space of nontrivial signature.
		Spinors are often described as "square roots of vectors" because the vector representation appears in the tensor product of two copies of the spinor representation.
	www.exampleproblems.com /wiki/index.php/Spinor (1004 words)

	Supergravity Summary
		In fact the gravitino field has one spinor and one vector index, which means that gravitinos transform as a tensor product of a spinorial representation and the vector representation of the Lorentz group.
		The available spinor representations depends on k; The maximal compact subgroup of the little group of the Lorentz group that preserves the momentum of a massless particle is Spin(d-1)× Spin(d-k-1), where k is equal to the number d of spatial dimensions minus the number d-k of time dimensions.
		Spinors in n-dimensions are representations (really modules) not only of the n-dimensional Lorentz group, but also of a Lie algebra called the n-dimensional Clifford algebra.
	www.bookrags.com /Supergravity (5185 words)

	[No title]
		Spinors are in a representation of its covering group $SL(2,C)$ (see~\cite{pct,bogoliubov}), but are not in general in a representation of the full Lorentz group, covered by what one call the $Pin(1,3)$ group~\cite{cdewitt} (and $Pin(3,1)$ for $O(3,1)$).
		A Majorana spinor is its own charge conjugated particle, which necessarily constrains this kind of particle to be neutral, and it must therefore obey the relation $\psi^c = \alpha \psi$ ($\alpha$ being a possible phase).
		The existence of a Majorana representation (which depends only on the metric signature), only implies the possible existence of Majorana spinors.}, $C_-$ is proportional to the identity (and thus $C_-$ can always be written in the form $C_-= \sqrt{{\bf c_-}} S^*S^{-1}$ where $S$ is any $4\times 4$ invertible matrix).
	perso.orange.fr /eric.chopin/latex/9805203b.txt (7177 words)

	CERN Courier - Ettore Majorana: genius and - IOP Publishing - article
		Ettore Majorana was born in Sicily in 1906.
		Majorana had explained to Fermi why the particle discovered by Joliot and Curie had to be as heavy as a proton, even while being electrically neutral.
		Majorana jotted down a new equation: for a chargeless particle like the neutrino, which is similar to the electron except for its lack of charge, only two components are needed to describe its movement in space-time - as if it uses two wheels (like a motorcycle).
	cerncourier.com /main/article/46/6/19 (2587 words)

	week93
		"Majorana spinors" describe spin-1/2 particles that come in both left-handed and right-handed forms and are their own antiparticle.
		The spinors we'll discuss are all representations of this group.
		But the number of physical degrees of freedom of a spinor field is half the number of (real) components of the spinor, since the Dirac equation relates the components.
	www.math.ucr.edu /home/baez/week93.html (3533 words)

	Spinor - CompWisdom (Site not responding. Last check: )
		The understanding of spinors as being attached to, and constructed from isotropic vectors in Euclidean spaces strongly suggests that a physical RÂ³ model of space in a fundamental physical theory be replaced with a CÂ³ that is the analytic continuation of RÂ³.
		It is an essential part of the assumptions in spinor fl magic that the RÂ³ model of physical space be physically considered as embedded in a complex CÂ³ mapped to the linear subspace of M(2, C) with vanishing trace.
		Spinors were invented by Wolfgang Pauli and Paul Dirac to describe the physical properties of spin, especially the properties of fermions whose spin numerically equals one half.
	www.compwisdom.com /topics/spinor (2389 words)

	[No title]
		"Majorana spinors" describe spin-1/2 particles that come in both left-handed and right-handed forms and are their own antiparticle.
		The point is that sometimes the Dirac spinors, or Majorana spinors, are a reducible representation of Spin(1,n-1).
		But the number of physical degrees of freedom of a spinor field is half the number of (real) components of the spinor, since the Dirac equation relates the components.
	math.ucr.edu /home/baez/twf_ascii/week93 (3585 words)

	Events archive (Site not responding. Last check: )
		The mechanism is based on the extension of ordinary superspace by an auxiliary commuting Majorana spinor allowing to construct Lorentz invariant supersymmetric derivatives without their statistic change.
		The Ramond vector appears in the composite form bilinear in the commuting spinor and ordinary grassmannian Majorana spinor which is the superpartner of the spacetime coordinates.
		The composite spinor form was earlier revealed by D.V. Volkov and the author and it clarifies the connection between spinning and supersymmetrical particles with spin half.
	ntserv.fys.ku.dk /nbiweb/formidling/page29215.htm?foredragid=3631&lang=en (382 words)

	Reference.com/Encyclopedia/Majorana equation
		If a particle has a spinor wavefunction ψ which satisfies the Majorana equation, then the quantity m in the equation is called the Majorana mass.
		Unlike Weyl spinors or Dirac spinors, the Majorana spinor is a real representation of the Lorentz group, which is why we are permitted to include both the spinor and its "complex conjugate" in the same equation.
		Actually, there is another way of writing a Majorana spinor in terms of four real components, which shows why the "complex conjugation" is sometimes referred to as an artifact of using the Dirac notation for a real spinor.
	www.reference.com /browse/wiki/Majorana_equation (224 words)

	Improvement of the Calculation of Scattering Amplitudes with External Fermions
		Spinors are in a representation of its covering group SL(2,C) (see [11][12]), but are not in general in a representation of the full Lorentz group, covered by what one call the Pin(1,3) group [13] (and Pin(3,1) for O(3,1)).
		A Majorana spinor is its own charge conjugated particle, which necessarily constrains this kind of particle to be neutral, and it must therefore obey the relation
		Another calculation technique was developed by Hagiwara and Zeppenfeld [21], decomposing spinors in the chiral representation into their Weyl spinors.
	perso.orange.fr /eric.chopin/latex/9805203.htm (3546 words)

	Cartan's Corner (using Charlotte Technology)
		The zero mean curvature surfaces in Majorana space have negative Gauss curvature (similar to minimal surfaces in Euclidean space), while the zero mean curvature surfaces in Lorentz space have a positive Gauss curvature (in contrast to minimal surfaces in Euclidean space).
		The eigenvectors of the 2-form are either vectors of eigenvalue zero, or isotropic complex Spinors (E. Cartan) of imaginary eigenvalues.
		The concepts of topological defects, Spinor eigenvectors, Falaco Solitons and non equilibrium Electromagnetic systems are combined to give a topological model for the classical and quantum features of the Photon.
	www22.pair.com /csdc/car/carhomep.htm (2569 words)

	spinor - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "spinor" is defined.
		Spinor : Eric Weisstein's World of Mathematics [home, info]
		Phrases that include spinor: dirac spinor, majorana-weyl spinor, majorana spinor, spinor group, weyl-majorana spinor, more...
	www.onelook.com /?w=spinor (101 words)

	Bookmarks [Kristjan Kannike]
		[hep-ph/0610174] Lepton Flavor Violating Decays as Probes of Neutrino Mass Spectra and Heavy Majorana Neutrino Masses
		[hep-ph/0603091] On the Quasi-fixed Point in the Running of CP-violating Phases of Majorana Neutrinos
		[hep-ph/0505226] The Absolute Neutrino Mass Scale, Neutrino Mass Spectrum, Majorana CP-Violation and Neutrinoless Double-Beta Decay
	www.physic.ut.ee /~kkannike/english/bookmarks.html (2751 words)

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