This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 | Archive 3 | → | Archive 5 |
Um, spinors are PROJECTIVE reps of SO(p,q) but (linear) reps of spin(p,q). In the section on spinors in various dimensions, you keep writing spin(N)/Z_2, at least for a group isomorphic to spin(N). Phys 02:42, 7 Aug 2004 (UTC)
I think this article could use some expanding, particularly in the overview, to make it more understandable by people who don't already know about spinors. It sometimes helps to explain the same thing a couple of different ways, so that people who are approaching the topic from different backgrounds can get it. It's a very good article otherwise though. Hope this helps.... —Preceding unsigned comment added by Spiralhighway ( talk • contribs) 17:01, 18 November 2004
Who uses instead of SO? I've never seen this before. _R_ 21:01, 1 Feb 2005 (UTC)
Ditto with Fropuff. The gothic lower case is standard notation. Most texts on differentiable manifolds will write, for instance, "Let be the Lie Algebra of a Lie Group G."-- Perkinsrc008 21:59, 8 June 2006 (UTC)
I think that Majorana particle should be its own page, rather than just a redirect to this particularly mathematical page. If there are no objections I will create a Majorana particle page at some point. -- Flying fish 05:10, 5 Jun 2005 (UTC)
Right. Gosh, I'd forgotten all this ... the reason that the Majorana spinor is "its own anti-particle" is precisely because it is a *real* representation; it doesn't have a distinct complex conjugate representation. So there's two ways of handling this. Amend the article to state something like a physical particle transforming under a real representation has the curious property that it is it's own antiparticle. Another possibility would be to start an article on the majorana particle that would detail some of the history of experimental searches for such beasties.
The reason that is self-conjugate is because its so again its "real"; conjugating it is a no-op. Alternately and SO(3) is "real", whereas SU(2) is complex (a doublet times a doublet is a triplet plus a singlet, fancy math talk for basic undergrad clebsch-gordon math) ...but this now walks down the slippery slope of having to explain what real and complex reps imply for physical properties of particles, and that's a whole nother mess ... linas 00:27, 7 Jun 2005 (UTC)
Is there any way this page can be made more understandable to the ordinary engineering graduate like me. It really is written only for the (math?) specialst at the moment. Can someone try to simplify please!-- Light current 01:32, 2 October 2005 (UTC)
...this article needs a cleanup. The intro. is ok at present, but more could be done to provide a better intuition of spinors (are there any diagrams, graphics that would help ?). The examples section is waaay too long and the example containing the long list towards the end is particularly ugly and definitely needs to be placed in a new article, perhaps spinors in relativity ? The content of the article is fine, just that it needs a better explanation of some of the maths to people who don't know too much about spinors (like me). --- Mpatel (talk) 13:55, 17 October 2005 (UTC)
The IPA pronunciation given in the article appears to be from British english (the lack of an 'r' gave it away to me; I'm American). Clearly "spinor" is pronounced with a hard 'r' at the end ;-) What I propose is that either the American pronunciation is added in addition to the British one, or the pronunciation simply be removed (I think it is pretty obvious how one should pronounce it in one's native accent). This is not the name of a person or something where the native pronunciation of the subject would be important. - Gauge 04:25, 24 October 2005 (UTC)
Surely it is not wise to give as an example of pronunciation perhaps the only word ('Linux') whose pronunciation, while correctly similar to spinor, is more hotly debated, and for the same reasons. Could we not say that the 'i' is pronounced like the 'i' in 'windows'? —Preceding unsigned comment added by 69.63.49.155 ( talk • contribs) 08:37, 22 November 2005
I thought the joke was funny, but now it just looks stupid in the article. Let's get rid of the whole pronunciation thing all together. -- Fropuff 17:28, 16 December 2005 (UTC)
The history of the study of spinors displays part of the intricate interplay between mathematics and physics over the last century. I believe that this article could benefit from teasing out this tangle. Give a potted history first, then the mathematical definitions and properties, then finally applications to physics.
As far as the mathematics goes, I believe that the study of spinors is eased somewhat by studying their relationship to Clifford algebras as well as Lie groups and Lie algebras. After Élie_Cartan [1], you could mention works by Claude Chevalley [2] ( [3] 1954); Marcel_Riesz [4]( [5] 1957, 1958, 1993); Michael Atiyah [6], Raoul_Bott [7] [8] and Arnold Shapiro ( [9] 1963); Ian Porteous [10] and Pertti Lounesto [11]. Porteous' two books "Topological Geometry" ( [12] 1969, [13]1981) and "Clifford Algebras and the Classical Groups" ( [14] 1995) explain the relationship between Clifford algebras and Lie groups with great care. Lounesto's book, "Clifford Algebras and Spinors" (1997, [15] 2001) makes the link between Clifford algebras and spinors very explicit.
See also Representations_of_Clifford_algebras. Leopardi 00:45, 14 February 2006 (UTC)
There is no definition to be found of what a spinor is, not even in the Mathematical details section, which is written as if spinor has already been made clear and ONLY the details need to be treated in isolation. Unfortunately my own understanding is limited and ungeneral. -- MarSch 11:23, 13 April 2006 (UTC)
Terry Bollinger 06:22, 31 December 2006 (UTC)
And spinors relate to quaternions how exactly? Are quaternions a kind of spinor or what? Francis Davey 21:16, 24 July 2007 (UTC)
The comment(s) below were originally left at Talk:Spinor/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
The Clebsch-Gordan stuff is probably too detailed for this article: suggest summary style. One or two sections are a bit stubby (e.g. the history) and could be expanded. Geometry guy 16:08, 7 September 2008 (UTC) |
Last edited at 16:08, 7 September 2008 (UTC). Substituted at 22:05, 3 May 2016 (UTC)
This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 | Archive 3 | → | Archive 5 |
Um, spinors are PROJECTIVE reps of SO(p,q) but (linear) reps of spin(p,q). In the section on spinors in various dimensions, you keep writing spin(N)/Z_2, at least for a group isomorphic to spin(N). Phys 02:42, 7 Aug 2004 (UTC)
I think this article could use some expanding, particularly in the overview, to make it more understandable by people who don't already know about spinors. It sometimes helps to explain the same thing a couple of different ways, so that people who are approaching the topic from different backgrounds can get it. It's a very good article otherwise though. Hope this helps.... —Preceding unsigned comment added by Spiralhighway ( talk • contribs) 17:01, 18 November 2004
Who uses instead of SO? I've never seen this before. _R_ 21:01, 1 Feb 2005 (UTC)
Ditto with Fropuff. The gothic lower case is standard notation. Most texts on differentiable manifolds will write, for instance, "Let be the Lie Algebra of a Lie Group G."-- Perkinsrc008 21:59, 8 June 2006 (UTC)
I think that Majorana particle should be its own page, rather than just a redirect to this particularly mathematical page. If there are no objections I will create a Majorana particle page at some point. -- Flying fish 05:10, 5 Jun 2005 (UTC)
Right. Gosh, I'd forgotten all this ... the reason that the Majorana spinor is "its own anti-particle" is precisely because it is a *real* representation; it doesn't have a distinct complex conjugate representation. So there's two ways of handling this. Amend the article to state something like a physical particle transforming under a real representation has the curious property that it is it's own antiparticle. Another possibility would be to start an article on the majorana particle that would detail some of the history of experimental searches for such beasties.
The reason that is self-conjugate is because its so again its "real"; conjugating it is a no-op. Alternately and SO(3) is "real", whereas SU(2) is complex (a doublet times a doublet is a triplet plus a singlet, fancy math talk for basic undergrad clebsch-gordon math) ...but this now walks down the slippery slope of having to explain what real and complex reps imply for physical properties of particles, and that's a whole nother mess ... linas 00:27, 7 Jun 2005 (UTC)
Is there any way this page can be made more understandable to the ordinary engineering graduate like me. It really is written only for the (math?) specialst at the moment. Can someone try to simplify please!-- Light current 01:32, 2 October 2005 (UTC)
...this article needs a cleanup. The intro. is ok at present, but more could be done to provide a better intuition of spinors (are there any diagrams, graphics that would help ?). The examples section is waaay too long and the example containing the long list towards the end is particularly ugly and definitely needs to be placed in a new article, perhaps spinors in relativity ? The content of the article is fine, just that it needs a better explanation of some of the maths to people who don't know too much about spinors (like me). --- Mpatel (talk) 13:55, 17 October 2005 (UTC)
The IPA pronunciation given in the article appears to be from British english (the lack of an 'r' gave it away to me; I'm American). Clearly "spinor" is pronounced with a hard 'r' at the end ;-) What I propose is that either the American pronunciation is added in addition to the British one, or the pronunciation simply be removed (I think it is pretty obvious how one should pronounce it in one's native accent). This is not the name of a person or something where the native pronunciation of the subject would be important. - Gauge 04:25, 24 October 2005 (UTC)
Surely it is not wise to give as an example of pronunciation perhaps the only word ('Linux') whose pronunciation, while correctly similar to spinor, is more hotly debated, and for the same reasons. Could we not say that the 'i' is pronounced like the 'i' in 'windows'? —Preceding unsigned comment added by 69.63.49.155 ( talk • contribs) 08:37, 22 November 2005
I thought the joke was funny, but now it just looks stupid in the article. Let's get rid of the whole pronunciation thing all together. -- Fropuff 17:28, 16 December 2005 (UTC)
The history of the study of spinors displays part of the intricate interplay between mathematics and physics over the last century. I believe that this article could benefit from teasing out this tangle. Give a potted history first, then the mathematical definitions and properties, then finally applications to physics.
As far as the mathematics goes, I believe that the study of spinors is eased somewhat by studying their relationship to Clifford algebras as well as Lie groups and Lie algebras. After Élie_Cartan [1], you could mention works by Claude Chevalley [2] ( [3] 1954); Marcel_Riesz [4]( [5] 1957, 1958, 1993); Michael Atiyah [6], Raoul_Bott [7] [8] and Arnold Shapiro ( [9] 1963); Ian Porteous [10] and Pertti Lounesto [11]. Porteous' two books "Topological Geometry" ( [12] 1969, [13]1981) and "Clifford Algebras and the Classical Groups" ( [14] 1995) explain the relationship between Clifford algebras and Lie groups with great care. Lounesto's book, "Clifford Algebras and Spinors" (1997, [15] 2001) makes the link between Clifford algebras and spinors very explicit.
See also Representations_of_Clifford_algebras. Leopardi 00:45, 14 February 2006 (UTC)
There is no definition to be found of what a spinor is, not even in the Mathematical details section, which is written as if spinor has already been made clear and ONLY the details need to be treated in isolation. Unfortunately my own understanding is limited and ungeneral. -- MarSch 11:23, 13 April 2006 (UTC)
Terry Bollinger 06:22, 31 December 2006 (UTC)
And spinors relate to quaternions how exactly? Are quaternions a kind of spinor or what? Francis Davey 21:16, 24 July 2007 (UTC)
The comment(s) below were originally left at Talk:Spinor/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
The Clebsch-Gordan stuff is probably too detailed for this article: suggest summary style. One or two sections are a bit stubby (e.g. the history) and could be expanded. Geometry guy 16:08, 7 September 2008 (UTC) |
Last edited at 16:08, 7 September 2008 (UTC). Substituted at 22:05, 3 May 2016 (UTC)