en>Bgwhite: WP:CHECKWIKI error fix #69. ISBN problem. Do general fixes and cleanup if needed. - using AWB (10638)

2015-01-03T03:32:42Z

WP:CHECKWIKI error fix #69. ISBN problem. Do general fixes and cleanup if needed. - using AWB (10638)

en>Wavelength: inserting 1 hyphen: —> "three- or four-dimensional"—wikt:three-dimensional—wikt:four-dimensional—WP:HYPHEN, sub-subsection 3, point 7 on hanging hyphens

2014-03-04T00:45:47Z

inserting 1 hyphen: —> "three- or four-dimensional"—wikt:three-dimensional—wikt:four-dimensional—WP:HYPHEN, sub-subsection 3, point 7 on hanging hyphens

Show changes

en>Bhny: WP:REFERS

2014-01-27T03:52:53Z

WP:REFERS

← Older revision		Revision as of 05:52, 27 January 2014
Line 1:		Line 1:
	~~The individual who wrote~~ the ~~article~~ is called ~~Jayson Hirano and he totally digs that title~~. ~~Distributing production~~ is ~~exactly where her primary earnings comes from~~. ~~Mississippi~~ is ~~exactly where his house is. To play lacross is something he would never give up~~.<br><br>~~My web~~ page ~~... free psychic (~~[~~http~~://~~www~~.~~january-yjm~~.~~com~~/xe/~~index~~.~~php?mid~~=~~video&document_srl~~=~~158289 Full Guide~~])		In [[differential geometry]], given a [[spin structure]] on a ''n''-dimensional [[Riemannian manifold]] (''M, g'') a section of the [[spinor bundle]] '''S''' is called a '''spinor field'''. The [[complex vector bundle]]
			:<math>\pi_{\mathbf S}:{\mathbf S}\to M\,</math>
			is associated to the corresponding [[principal bundle]]
			:<math>\pi_{\mathbf P}:{\mathbf P}\to M\,</math>
			of spin frames over ''M'' via the [[spin representation]] of its structure group Spin(''n'') on the space of [[spinor]]s Δ<sub>''n''</sub>.

			==Formal definition==
			Let ('''P''', ''F''<sub>'''P'''</sub>) be a [[spin structure]] on a [[Riemannian manifold]] (''M, g'') that is, an [[equivariant]] lift of the oriented [[orthonormal frame bundle]] <math>\mathrm F_{SO}(M)\to M</math> with respect to the double covering <math>\rho: {\mathrm {Spin}}(n)\to {\mathrm {SO}}(n)\,.</math>

			One usually defines the [[spinor bundle]]<ref>{{citation \| last1=Friedrich\|first1=Thomas\|title = Dirac Operators in Riemannian Geometry\| year=2000\|page=53}}</ref> <math>\pi_{\mathbf S}:{\mathbf S}\to M\,</math> to be the [[complex vector bundle]]
			:<math>{\mathbf S}={\mathbf P}\times_{\kappa}\Delta_n\,</math>

			associated to the [[spin structure]] '''P''' via the [[spin representation]] <math>\kappa: {\mathrm {Spin}}(n)\to {\mathrm U}(\Delta_n),\,</math> where U('''W''') denotes the [[Group (mathematics)\|group]] of [[unitary operator]]s acting on a [[Hilbert space]] '''W'''.

			A '''spinor field''' is defined to be a section of the [[spinor bundle]] '''S''', i.e., a smooth mapping <math>\psi : M \to {\mathbf S}\,</math> such that <math>\pi_{\mathbf S}\circ\psi: M\to M\,</math>
			is the identity mapping id<sub>''M''</sub> of ''M''.

			==See also==
			* [[Orthonormal frame bundle]]
			* [[Spinor]]
			* [[Spin manifold]]
			* [[Spinor representation]]
			* [[Spin geometry]]

			==Notes==
			{{Reflist}}

			==Books==
			* {{Cite book \| last1=Lawson \| first1=H. Blaine \| last2=Michelsohn \| first2=Marie-Louise \|author2-link=Marie-Louise Michelsohn\| title=Spin Geometry \| publisher=[[Princeton University Press]] \| isbn=978-0-691-08542-5 \| year=1989 \| postscript=<!--None-->}}
			* {{citation \| last1=Friedrich\|first1=Thomas\| title = Dirac Operators in Riemannian Geometry\| publisher=[[American Mathematical Society]] \| year=2000\|isbn=978-0-8218-2055-1}}

			[[Category:Riemannian geometry]]
			[[Category:Structures on manifolds]]
			[[Category:Algebraic topology]]
			[[Category:Quantum field theory]]
			[[Category:Spinors]]

			{{differential-geometry-stub}}

			[[ca:Fibrat d'espinors]]
			[[es:Fibrado de espinores]]
			[[zh:旋量丛]]

en>John of Reading: Typo and General fixing, typos fixed: traditionnally → traditionally, i.e → i.e. (2) using AWB (8097)

2012-07-27T16:03:41Z

Typo and General fixing, typos fixed: traditionnally → traditionally, i.e → i.e. (2) using AWB (8097)

New page

The individual who wrote the article is called Jayson Hirano and he totally digs that title. Distributing production is exactly where her primary earnings comes from. Mississippi is exactly where his house is. To play lacross is something he would never give up.<br><br>My web page ... free psychic ([http://www.january-yjm.com/xe/index.php?mid=video&document_srl=158289 Full Guide])

Spatial analysis - Revision history

en>Bgwhite: WP:CHECKWIKI error fix #69. ISBN problem. Do general fixes and cleanup if needed. - using AWB (10638)

en>Wavelength: inserting 1 hyphen: —> "three- or four-dimensional"—wikt:three-dimensional—wikt:four-dimensional—WP:HYPHEN, sub-subsection 3, point 7 on hanging hyphens

en>Bhny: WP:REFERS

en>John of Reading: Typo and General fixing, typos fixed: traditionnally → traditionally, i.e → i.e. (2) using AWB (8097)