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Spinors in three dimensions information


In mathematics, the spinor concept as specialised to three dimensions can be treated by means of the traditional notions of dot product and cross product. This is part of the detailed algebraic discussion of the rotation group SO(3).

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Spinors in three dimensions

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of spinors that a student of physics encounters are the 2×1 spinors used in Pauli's theory of electron spin. The Pauli matrices are a vector of three 2×2...

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Spinor

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class. Spinors can be exhibited as concrete objects using a choice of Cartesian coordinates. In three Euclidean dimensions, for instance, spinors can be...

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Outer product

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spineurs, translated 1966: The Theory of Spinors, Hermann, Paris Pertti Lounesto (1997) Clifford Algebras and Spinors, page 51, Cambridge University Press...

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Rotation formalisms in three dimensions

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In geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to...

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Pauli matrices

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decomposition of a single-qubit gate. Algebra of physical space Spinors in three dimensions Gamma matrices § Dirac basis Angular momentum Gell-Mann matrices...

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Point groups in three dimensions

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In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry...

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Isotropic line

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expanded the concept of isotropic lines to multivectors in his book on spinors in three dimensions. Edmond Laguerre (1870) "Sur l’emploi des imaginaires...

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Ising model

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theory. The spin and energy correlation functions are described by a minimal model, which has been exactly solved. In three as in two dimensions, the most...

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Angular acceleration

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angular speed increases clockwise or decreases counterclockwise. In three dimensions, angular acceleration is a pseudovector. For rigid bodies, angular...

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Superstring theory

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currently restrict the spinors to 32-components—which limits the number of dimensions to 11 (or 12 if you include two time dimensions.) Some physicists (e...

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Superspace

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a spinor under the Poincaré subalgebra. In four dimensions there are three distinct irreducible 4-component spinors. There is the Majorana spinor, the...

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Dimensions in Time

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Dimensions in Time is a charity special crossover between the British science fiction television series Doctor Who and the soap opera EastEnders. The...

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String theory

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theories in two or three spacetime dimensions are useful for describing phenomena in condensed matter physics. Finally, there exist scenarios in which there...

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Spin representation

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of a spin representation are called spinors. They play an important role in the physical description of fermions such as the electron. The spin representations...

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Dimension

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each other to annihilate at a meaningful rate in three dimensions, so it follows that only three dimensions of space are allowed to grow large given this...

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Vasiliev equations

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of variations of Vasiliev equations that work in three, four and arbitrary number of space-time dimensions. Vasiliev's equations admit supersymmetric extensions...

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Spin group

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conjugate spinors span W ¯ {\displaystyle {\overline {W}}} . It is straightforward to see that the spinors anti-commute, and that the product of a spinor and...

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Space group

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In mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements...

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Rotation

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applies to rotations in two dimensions (in a plane), in which exactly one point is kept fixed; and also in three dimensions (in space), in which additional...

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Quaternionic representation

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In physics, one often encounters the spinors of Spin(d, 1). These representations have the same type of real or quaternionic structure as the spinors...

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