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- Spin_representation abstract "In mathematics, the spin representations are particular projective representations of the orthogonal or special orthogonal groups in arbitrary dimension and signature (i.e., including indefinite orthogonal groups). More precisely, they are representations of the spin groups, which are double covers of the special orthogonal groups. They are usually studied over the real or complex numbers, but they can be defined over other fields.Elements 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 may be constructed in several ways, but typically the construction involves (perhaps only implicitly) the choice of a maximal isotropic subspace in the vector representation of the group. Over the real numbers, this usually requires using a complexification of the vector representation. For this reason, it is convenient to define the spin representations over the complex numbers first, and derive real representations by introducing real structures.The properties of the spin representations depend, in a subtle way, on the dimension and signature of the orthogonal group. In particular, spin representations often admit invariant bilinear forms, which can be used to embed the spin groups into classical Lie groups. In low dimensions, these embeddings are surjective and determine special isomorphisms between the spin groups and more familiar Lie groups; this elucidates the properties of spinors in these dimensions.".
- Spin_representation wikiPageExternalLink QFT.
- Spin_representation wikiPageID "10160091".
- Spin_representation wikiPageLength "32948".
- Spin_representation wikiPageOutDegree "91".
- Spin_representation wikiPageRevisionID "678772634".
- Spin_representation wikiPageWikiLink Antihomomorphism.
- Spin_representation wikiPageWikiLink Bilinear_form.
- Spin_representation wikiPageWikiLink Bilinear_map.
- Spin_representation wikiPageWikiLink Cartan_subalgebra.
- Spin_representation wikiPageWikiLink Cartan_subgroup.
- Spin_representation wikiPageWikiLink Category:Representation_theory_of_Lie_groups.
- Spin_representation wikiPageWikiLink Category:Spinors.
- Spin_representation wikiPageWikiLink Classical_group.
- Spin_representation wikiPageWikiLink Clifford_algebra.
- Spin_representation wikiPageWikiLink Clifford_module.
- Spin_representation wikiPageWikiLink Commutator.
- Spin_representation wikiPageWikiLink Complex_number.
- Spin_representation wikiPageWikiLink Complexification.
- Spin_representation wikiPageWikiLink Connected_space.
- Spin_representation wikiPageWikiLink Covering_group.
- Spin_representation wikiPageWikiLink Degenerate_bilinear_form.
- Spin_representation wikiPageWikiLink Dimension.
- Spin_representation wikiPageWikiLink Dimension_(vector_space).
- Spin_representation wikiPageWikiLink Dirac_spinor.
- Spin_representation wikiPageWikiLink Dual_representation.
- Spin_representation wikiPageWikiLink Dual_space.
- Spin_representation wikiPageWikiLink Electron.
- Spin_representation wikiPageWikiLink Embedding.
- Spin_representation wikiPageWikiLink Equivariant_map.
- Spin_representation wikiPageWikiLink Exterior_algebra.
- Spin_representation wikiPageWikiLink Fermion.
- Spin_representation wikiPageWikiLink Field_(mathematics).
- Spin_representation wikiPageWikiLink General_linear_group.
- Spin_representation wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Spin_representation wikiPageWikiLink Group_homomorphism.
- Spin_representation wikiPageWikiLink Group_isomorphism.
- Spin_representation wikiPageWikiLink Identity_element.
- Spin_representation wikiPageWikiLink Indefinite_orthogonal_group.
- Spin_representation wikiPageWikiLink Interior_product.
- Spin_representation wikiPageWikiLink Invariant_(mathematics).
- Spin_representation wikiPageWikiLink Involution_(mathematics).
- Spin_representation wikiPageWikiLink Irreducible_representation.
- Spin_representation wikiPageWikiLink Isomorphism.
- Spin_representation wikiPageWikiLink Isotropic_quadratic_form.
- Spin_representation wikiPageWikiLink Kernel_(algebra).
- Spin_representation wikiPageWikiLink Lie_algebra.
- Spin_representation wikiPageWikiLink Lie_algebra_representation.
- Spin_representation wikiPageWikiLink Lie_group.
- Spin_representation wikiPageWikiLink Linear_map.
- Spin_representation wikiPageWikiLink Mathematics.
- Spin_representation wikiPageWikiLink Metric_signature.
- Spin_representation wikiPageWikiLink Opposite_category.
- Spin_representation wikiPageWikiLink Orthogonal_group.
- Spin_representation wikiPageWikiLink Parity_(mathematics).
- Spin_representation wikiPageWikiLink Physics.
- Spin_representation wikiPageWikiLink Polarization_identity.
- Spin_representation wikiPageWikiLink Projective_representation.
- Spin_representation wikiPageWikiLink Quadratic_form.
- Spin_representation wikiPageWikiLink Real_number.
- Spin_representation wikiPageWikiLink Real_representation.
- Spin_representation wikiPageWikiLink Real_structure.
- Spin_representation wikiPageWikiLink Representation_of_a_Lie_group.
- Spin_representation wikiPageWikiLink Root_system.
- Spin_representation wikiPageWikiLink Schurs_lemma.
- Spin_representation wikiPageWikiLink Simple_module.
- Spin_representation wikiPageWikiLink Spin_group.
- Spin_representation wikiPageWikiLink Spinor.
- Spin_representation wikiPageWikiLink Springer_Science+Business_Media.
- Spin_representation wikiPageWikiLink Subgroup.
- Spin_representation wikiPageWikiLink Surjective_function.
- Spin_representation wikiPageWikiLink Sylvesters_law_of_inertia.
- Spin_representation wikiPageWikiLink Symmetric_bilinear_form.
- Spin_representation wikiPageWikiLink Vector_space.
- Spin_representation wikiPageWikiLink Weight_(representation_theory).
- Spin_representation wikiPageWikiLinkText "Spin representation".
- Spin_representation wikiPageWikiLinkText "spin representation".
- Spin_representation wikiPageUsesTemplate Template:=.
- Spin_representation wikiPageUsesTemplate Template:Citation.
- Spin_representation wikiPageUsesTemplate Template:Langle.
- Spin_representation wikiPageUsesTemplate Template:Math.
- Spin_representation wikiPageUsesTemplate Template:Rangle.
- Spin_representation wikiPageUsesTemplate Template:Reflist.
- Spin_representation subject Category:Representation_theory_of_Lie_groups.
- Spin_representation subject Category:Spinors.
- Spin_representation hypernym Representations.
- Spin_representation type Colour.
- Spin_representation type Algebra.
- Spin_representation type Physic.
- Spin_representation comment "In mathematics, the spin representations are particular projective representations of the orthogonal or special orthogonal groups in arbitrary dimension and signature (i.e., including indefinite orthogonal groups). More precisely, they are representations of the spin groups, which are double covers of the special orthogonal groups. They are usually studied over the real or complex numbers, but they can be defined over other fields.Elements of a spin representation are called spinors.".
- Spin_representation label "Spin representation".
- Spin_representation sameAs Q17103552.
- Spin_representation sameAs m.02q3rnn.
- Spin_representation sameAs Q17103552.
- Spin_representation wasDerivedFrom Spin_representation?oldid=678772634.
- Spin_representation isPrimaryTopicOf Spin_representation.