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- ...[[linear combination]] of ''products of the bilinears'' of the individual spinors. It is named after Swiss physicist [[Markus Fierz]]. The Fierz identities a The signs in the table correspond to the case of ''commuting spinors'', otherwise, as is the case of fermions in physics, ''all coefficients ch ...5 Кб (740 слов) - 13:31, 7 марта 2024
- ...vated by the need to form well-behaved, measurable quantities out of Dirac spinors, replacing the usual role of the [[Hermitian adjoint]]. == Spinors under Lorentz transformations == ...4 Кб (461 слово) - 16:32, 27 февраля 2024
- ==Spinors== Put it more explicitly, the Dirac spinors in the helicity basis for a fermion is ...5 Кб (783 слова) - 10:57, 20 марта 2024
- {{Short description|Matrices used for Lorentz group spinors}} ...iplication]] of covectors on left handed [[spinors]] giving a right-handed spinors or vice versa, i.e. they are off diagonal blocks of [[gamma matrices]]. The ...9 Кб (1391 слово) - 01:15, 26 марта 2024
- *''Twistor and Killing spinors on [[Riemannian manifold]]s'', with Thomas Friedrich, Ralf Grunewald, and I <ref name=twist>Review of ''Twistor and Killing spinors on Riemannian manifolds'': N. J. Hitchin, {{MR|1084369}}</ref> ...4 Кб (379 слов) - 10:35, 20 марта 2024
- ...equation]] without complex numbers, and its elements are called Majorana [[spinors]]. ...ation|first=Pierre|last=Deligne|authorlink=Pierre Deligne|chapter=Notes on spinors |title= Quantum Fields and Strings: A Course for Mathematicians |editor-fir ...4 Кб (571 слово) - 17:25, 19 февраля 2024
- ...first2=J. | title=Spontaneously broken supergauge symmetries and goldstone spinors | journal=Physics Letters B | publisher=Elsevier BV | volume=51 | issue=5 | ...2 Кб (163 слова) - 23:36, 6 марта 2024
- ...a particle. Strictly speaking, they are not vectors at all, but in fact [[spinors]]. For a single spin 1/2 particle, they can be defined as the [[eigenvecto ...ritten as a [[linear combination]] of the [[basis (linear algebra)|basis]] spinors. ...5 Кб (661 слово) - 12:23, 2 марта 2024
- ...sions]].<ref>{{Citation | last1=Cartan | first1=Élie | title=The theory of spinors | origyear=1938 | url=https://books.google.com/books?isbn=0486640701 |page= ...5 Кб (663 слова) - 08:54, 27 марта 2024
- ...can all be expressed directly in terms of the [[Ricci spinors]] and [[Weyl spinors]], using [[Newman–Penrose formalism]]; see the link below. ...5 Кб (685 слов) - 08:28, 15 февраля 2024
- ...ns to the [[Dirac equation]] for spinor fields are often called ''harmonic spinors''.<ref>{{SpringerEOM|id=Spinor_structure&oldid=33893 |title=Spinor structur ...l=https://books.google.com/books?id=FzcbAQAAIAAJ |title=An Introduction to Spinors and Geometry with Applications in Physics |last2=Tucker |first2=Robin W. |d ...9 Кб (1284 слова) - 16:33, 27 февраля 2024
- {{Short description|Mathematical notation for tensors and spinors}} ...="Penrose1984">{{Cite book |last=Roger Penrose and Wolfgang Rindler |title=Spinors and Space-Time, Volume 1: Two-Spinor Calculus and Relativistic Fields |publ ...8 Кб (1123 слова) - 03:52, 28 декабря 2023
- ...geometry]]. For example, effectively all [[Riemannian manifold]]s can have spinors and [[spin connection]]s built upon them, via the [[Clifford algebra]].<ref ...ion. The chiral spinors may be written as linear combinations of the Dirac spinors presented below; thus, nothing is lost or gained, other than a change in pe ...24 Кб (3593 слова) - 16:33, 27 февраля 2024
- ...an der Waerden notation]], distinguishes left-handed and right-handed Weyl spinors from each other. Generators of other spin, such spin-3/2 or higher, are dis ...tion operator]] rather than Pauli matrices used for the two-component Weyl spinors.<ref>{{cite book|last=Năstase|first=H.|author-link=|date=2015|title=Introd ...11 Кб (1554 слова) - 11:52, 18 марта 2024
- ...presentation|representation]] of the action of the [[Clifford algebra]] on spinors. ...and its complex conjugate contains a top-dimensional component. Such pure spinors determine generalized almost complex structures. ...21 Кб (3108 слов) - 00:37, 12 марта 2024
- ...same decomposition holds for the compact form as well: the product of two spinors in [[SU(2)|su(2)]] being a vector in the [[rotation group]] [[O(3)]] and a ...9 Кб (1310 слов) - 21:09, 16 февраля 2024
- ==Spinors== ...9 Кб (1224 слова) - 22:11, 14 марта 2024
- ...one always counts the number of ''real'' irreducible representations. The spinors with spins less than 3/2 that exist in each number of dimensions will be cl == A classification of spinors == ...28 Кб (4164 слова) - 11:26, 21 марта 2024
- ...tilized in relativistically invariant wave equations for fermions (such as spinors) in arbitrary space-time dimensions, notably in string theory and supergra {{Cite journal | last1=Petitjean | first1=Michel | title=Chirality of Dirac spinors revisited | journal=Symmetry | year=2020 | volume=12 | issue=4 | pages=616 ...27 Кб (3786 слов) - 11:26, 21 марта 2024
- * {{cite journal | last=Bär | first=Christian | title=Real Killing spinors and holonomy | journal=[[Communications in Mathematical Physics]] | publish ...3 Кб (370 слов) - 09:45, 18 февраля 2024