spinor oor Grieks
spinor
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(algebra) An element of the fundamental representation of a Clifford algebra
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non-tensorial representation of the spin group; represents fermions in physics
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The most general mathematical form of spinors was discovered by Élie Cartan in 1913.
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If the vector space V has extra structure that provides a decomposition of its complexification into two maximal isotropic subspaces, then the definition of spinors (by either method) becomes natural.
Μην καταψύχετεWikiMatrix WikiMatrix
More specifically, instead of representing spinors as complex-valued 2D column vectors as Pauli had done, they represented them as complex-valued 2 × 2 matrices in which only the elements of the left column are non-zero.
Είναι στο δρόμο μουWikiMatrix WikiMatrix
The even subalgebra Cl02,0(R), spanned by even-graded basis elements of Cl2,0(R), determines the space of spinors via its representations.
Και παιδικά βυζάκιαWikiMatrix WikiMatrix
Spinors were first applied to mathematical physics by Wolfgang Pauli in 1927, when he introduced his spin matrices.
Οι Δύο ΠύργοιWikiMatrix WikiMatrix
The following year, Paul Dirac discovered the fully relativistic theory of electron spin by showing the connection between spinors and the Lorentz group.
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The equivalence of these constructions are a consequence of the uniqueness of the spinor representation of the complex Clifford algebra.
Με άκουσες, κ. Μπίσοπ; Γιατί δεν κινούμαιWikiMatrix WikiMatrix
Scalar fields are contrasted with other physical quantities such as vector fields, which associate a vector to every point of a region, as well as tensor fields and spinor fields.
Δεν είναι επιλέξιμες οι δαπάνες που έχουν εκτελεστεί πριν την ημερομηνία κατά την οποία η Επιτροπή λαμβάνει τη σχετική αίτηση συνδρομήςWikiMatrix WikiMatrix
The spinor/quaternion representation of rotations in 3D is becoming increasingly prevalent in computer geometry and other applications, because of the notable brevity of the corresponding spin matrix, and the simplicity with which they can be multiplied together to calculate the combined effect of successive rotations about different axes.
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If this happens in an even dimension, the Majorana spinor representation will sometimes decompose into two Majorana–Weyl spinor representations.
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In some sense they describe the "square root" of geometry and, just as understanding the square root of −1 took centuries, the same might be true of spinors.
AND (δινιτραμιδικό αμμώνιο ή SR #) (CASWikiMatrix WikiMatrix
This is an essential feature of Dirac's theory, which ties the spinor formalism to the geometry of physical space.
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Some simple examples of spinors in low dimensions arise from considering the even-graded subalgebras of the Clifford algebra Clp, q(R).
Εργασίες θεμελιώσεων # εργασίες διάνοιξης φρεάτων ύδατοςWikiMatrix WikiMatrix
The word "spinor" was coined by Paul Ehrenfest in his work on quantum physics.
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Once again, the problem of lifting a vector rotation to a spinor rotation is two-valued: the expression (1) with (180° + θ/2) in place of θ/2 will produce the same vector rotation, but the negative of the spinor rotation.
Εσύ τον φλερτάρεις, τον φέρνεις εδώ μετά το δείπνο... τον οδηγείς σε κατάσταση ικανοποίησης και εγώ θα του ρίξωWikiMatrix WikiMatrix
In addition, sometimes the non-complexified version of Clp,q(R) has a smaller real representation, the Majorana spinor representation.
Είπες ότι πήγαινες με #;- Είπα, ότι πήγαινα μεWikiMatrix WikiMatrix
In 1 dimension (a trivial example), the single spinor representation is formally Majorana, a real 1-dimensional representation that does not transform.
Παίκτης #, επίπεδοWikiMatrix WikiMatrix
One can explicitly construct the spinors, and then examine how they behave under the action of the relevant Lie groups.
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In physics terms, this shows that Δ is built up like a Fock space by creating spinors using anti-commuting creation operators in W acting on a vacuum ω.
Εφόσον στο πρόγραμμα ασφάλειας αερομεταφορέα περιγράφονται οι μέθοδοι και οι διαδικασίες που θα ακολουθεί ο αερομεταφορέας για τη συμμόρφωσή του με τις απαιτήσεις του κανονισμού (ΕΚ) αριθ. #/# και των πράξεων εφαρμογής του, ο αερομεταφορέας είναι δυνατόν να θεωρηθεί ότι πληροί τις απαιτήσεις των στοιχείων α) και β) για όλες τις εγκαταστάσεις που προσδιορίζονται στο πρόγραμμαWikiMatrix WikiMatrix
An important feature of this definition is the distinction between ordinary vectors and spinors, manifested in how the even-graded elements act on each of them in different ways.
Αυτό είναι το πρόβλημαWikiMatrix WikiMatrix
In other notable early work, Rarita and Schwinger formulated the abstract Pauli and Fierz theory of the spin 3/2 field in a concrete form, as a vector of Dirac spinors.
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The most typical type of spinor, the Dirac spinor, is an element of the fundamental representation of Clp+q(C), the complexification of the Clifford algebra Clp, q(R), into which the spin group Spin(p, q) may be embedded.
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All the properties of spinors, and their applications and derived objects, are manifested first in the spin group.
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Concrete representations involving the Pauli matrices and more general gamma matrices are an integral part of the physical description of fermions, which behave as spinors.
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Quote from Elie Cartan: The Theory of Spinors, Hermann, Paris, 1966, first sentence of the Introduction section of the beginning of the book (before the page numbers start): "Spinors were first used under that name, by physicists, in the field of Quantum Mechanics.
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