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Somebody should redirect Pauli Gate to go to this page, I have no experience doing this, and it wasn't as easy as #REDIRECT Pauli Gate so I didn't do it.
I removed this:
I don't see in what sense four matrices can "generate" an uncountable group, especially if they aren't even elements of that group. AxelBoldt 00:34 Apr 29, 2003 (UTC)
Looking at the replacement
I think I see the source of my confusion. We are not talking about generators in the sense of group theory, but rather "infinitesimal generators" of a Lie group, i.e. the elements of its Lie algebra. This should be clarified somewhere. So what we are really saying is that σ1,σ2 and σ3 form an R-basis of the Lie algebra su(2) of all Hermitian 2x2 matrices with trace 0, is that correct?
Also, the above link to group representation is misleading, since we are really representing a Lie algebra, not a group. I'll try to weave that into the article. AxelBoldt 20:02 Apr 29, 2003 (UTC)
I think the sign of has been inadvertently flipped. Indeed, I don't know what books y'all are looking at, but it at least some textbooks this guy does appear with the other sign.
Why is the other sign preferable? Self-consistency, but more for aesthetics than anything else. The problem is that with the present sign, multiplying by and exponentiating gives clockwise rotation, whereas give counterclockwise rotation. That's a bit awkward and is a minor annoyance in related articles like Lorentz group. OK, this might be my most pedantic quibble yet, but if anyone agrees the sign needs fixing, please do it (don't forget to check the commutators, which you'll probably also need to modify).--- CH (talk) 16:42, 13 July 2005 (UTC)
At this point, I feel, it may be useful to emphasize the anticommutator relations of the matrices as their defining equations. This clarifies their relationship to the invariant metric tensor defining SO(3) and their role in the corresponding Clifford algebra. This algebraic definition allows for a manifold of alternative representations. Please, have a look at the matrices for an analogy.
You may, of course, insist on etc. to keep conventions of chirality in 3-dimensional space.
Direct calculation shows that the Lie algebra su(2) is the 3 dimensional real algebra spanned by the set {i σj}.
What is meant by a real algebra here? Surely the elements of the set {i σj} are complex. Wiki me ( talk) 22:30, 27 February 2008 (UTC)
I think it may help eliminate confusion to use the normal convention of denoting Lie groups with uppercase letters and their corresponding Lie algebras with lowercase letters. I changed some instances that I noticed in the article. Thanks. Idempotent ( talk) 12:02, 1 August 2008 (UTC)
With regard to Quantum mechanics, would a section on probability of measurement of the electron's spin not be good/informative? —Preceding unsigned comment added by 92.236.96.97 ( talk) 12:25, 2 September 2008 (UTC)
I've tried printing the article as it stands, using four different printers, all of which print other Wikipedia articles OK, but for the Pauli Matrices article I find the Commutation relations (near top of 2nd page, printing as normal A4 in portrait orientation) don't come out, neither do the contents of the "Proof of (1)" box (lower on 2nd page), nor do parts of "Proof of (2)" box; and a single line for p = span{isigma1,isigma2}. Unless others find the printing is AOK, it would be nice if someone could amend this please (I'd rather not mess with it myself). Thanks PaulGEllis ( talk) 20:14, 7 September 2008 (UTC)
As a new reader (despite already knowing clifford algebra) I found the commutator section exceptionally unclear. The Pauli vector was defined, but only by context could one see the mechanism that it provided to relate a vector to a "Pauli vector".
Additionally the statement "(as long as the vectors a and b commute with the pauli matrixes)" was confusing since one doesn't ever directly multiple these R^3 vectors with these 2x2 matrixes.
I've attempted to clarify this, adding in a bit of the reverse engineering context that was required to understand the text. In doing so I've split the Pauli vector definition out of the commutator section.
As somebody who doesn't have any text that covers this material I can't comment on how well used the Pauli vector concept is. If one's aim is to learn how to use the matrix algebra (ie: for things like rotations that aren't even covered in this article), I'd be inclined to define a vector in terms of coordinates directly:
and omit (or defer to an afternote) the Pauli vector entirely.
Peeter.joot ( talk) 05:28, 6 December 2008 (UTC)
Isn't the Pauli algebra just the good ol' real algebra of 2 by 2 complex matrices? It seems worth to mention it, along with the much more exotic reference to the real Clifford algebra 3,0. 147.122.52.70 ( talk) 11:39, 20 April 2009 (UTC)
This article is far from being complete. The Pauli matrices play a big role in Quantum Information wich should be highlighted. This is a big mistake, because Quantum Information is one of the most clearest ways to understand Quantum Mechanics.
This article should have separated sections for the following three topics: 1) Connection of the Pauli matrices with quantum error correcting codes. 2) Information about the generalised Pauli group: pauli matrices can be defined for any finite group (abelian or not). 3) The stabiliser formalism and the Gottesman-Knill theorem! Relation to Clifford operations! — Preceding unsigned comment added by Garrapito ( talk • contribs) 02:22, 18 June 2011 (UTC)
Here it should be mentioned that this is the quantum-mechanics of the simple alternative (eigenvalues +1,-1), i.e. the lowest-dimensional non-trivial quantum-mechanics (in Hilbert-space C2). This was used by Carl-Friedrich von Weizsäcker for his Ur-theory - Urs are the basic two elementary particles in this theory, corresponding to the two inequivalent representations mentioned here. Mathematically - thanks for mentioning the Clifford-algebra here. The Pauli-matrices generate the real, associative Clifford-algebra over an Euclidean R3 (defined by a positive-definite real bilinear-form). There is an alternative on R3 with respect to an indefinite non-degenerate bilinear-form of signature (++-), with a two-dimensional representation by complex 2x2 matrices. These are given by an alternative to the Pauli-matrices, changing some signs. Another mathematical remark: With respect to the canonical bilinear-form trace(AB)-trace(A)trace(B) for matrices A,B ∈ Cn,n (i.e. square matrices), the 4-dimensional real vector-space, spanned by the 2x2 identity-matrix and the three Pauli-matrices is a real Minkowski-space with signature (+---). Sofar there is no physical meaning behind this, it is just „Zufall", like the other one, namely that the only unit-spheres Sn that are Lie-groups are those for n=1 and n=3. Taking the above alternative to the Pauli-matrices, this signature on the four dimensional vector-space becomes (++--). — Preceding unsigned comment added by 130.133.155.70 ( talk) 13:51, 24 September 2012 (UTC)
Thus Fropuff's isomorphism above not only is one of 4-dimensional real vector-spaces, but also one of Minkowski-spaces.
There is another remark above: Certainly there is an equality of this Clifford-algebra to the general linear complex algebra of endomorphisms of C2. The proof even is easy, it suffices to show, that the matrices you get by matrix multiplication are linearly independent. But - this remark also is misleading, since both associative algebras have n-dimensional generalizations, and these are not isomorphic for higher dimensions, for instance in the case of Dirac-matrices. Relativistic physics neads Dirac matrices, which with respect to the above bilinear-form of matrices are a Minkowski-space as well. The same holds for the Duffin-Kemmer-Petiau matrices. So referring to this isomorphism makes sense only for the 2-dimensional case, corresponding to the fact, that simple Lie (and Jordan) algebras of lower dimensions collapse to only a few isomorphism classes.
Let me add, that the Clifford-algebras are universal envelops of a class of Jordan-algebras, defined by the underlying non-degenerate symmetric bilinear-forms in the same way, as the Heisenberg Lie-algebras are defined in terms of symplectic forms. Thus Bose-Einstein and Fermi-Dirac creation and annihilation operators are traced back to the two types of non-degenerate bilinear forms, the symmetric and the skew ones (and therefore there is no third type of statistics).
As the Pauli matrices were developed in the study of spin 1/2 particles, I think the article should have a physics bias. I'd propose that the explanation of their use in physics be moved to be more prominent, and the interpretation of the two-component vectors/spinors be explained. If I understand rightly, each spinor corresponds to a point on the sphere, and is the state of the system with a definite spin in that direction. The components map to the Riemann sphere by dividing one component by the other. Explaining this in the article would explain how to find eigenvectors of linear combinations of Pauli matrices, which is important as these are the observable states for the observables these combinations represent. At the moment, the article only explains the eigenvectors of the Pauli matrices themselves. Count Truthstein ( talk) 17:11, 29 November 2012 (UTC)
I think the problem comes from the fact that there are multiple choices for generators of the Lie algebra su(2). Looking at Special unitary group: n = 2, we see that the algebra is generated by u1, u2 and u3 with [u1,u2] = u3 and cyclic permutations of the indices. The most obvious relation to the Pauli matrices (from the definitions of the matrices in this article, and using their commutation relations) would be to have ui = −i σi. However, as is apparent at the other article, u1 = i σ1,u2 = −i σ2 and u3 = i σ3 works as well, with an unexpected minus sign on the second matrix (the minus sign could of course be on any of the matrices). Count Truthstein ( talk) 17:03, 9 March 2013 (UTC)
An IP made this , and I reverted since there didn't appear to be any problem at all before the indents were removed. it looks odd to have some formulae not indented and pressed against the screen, and the rest indented. Can anyone confirm any technical problems of this nature? Thanks, M∧Ŝ c2ħε Иτlk 07:01, 4 May 2013 (UTC)
Shouldn't the lead section be shorter? -- Mortense ( talk) 11:32, 27 December 2014 (UTC)
How about moving the higher spin matrices, without the ħ, of course, to Rotation group SO(3)#A note on representations? Higher spins hardly belong here. Concerning the arbitrary j case commented out, how about indexing a from 1 to 2j+1, as the novice would expect, in which case Jz = (j+1−a) δb,a, and the J± added and subtracted to have Jx and Jy, which are more familiar? E.g., Jx = (δb,a+1+δb+1,a) √(j+1)(a+b−1)−ab /2, which agrees with the examples. I don't presume to foist work orders on the commentor, though... Cuzkatzimhut ( talk) 17:03, 9 January 2015 (UTC)
The higher-spin matrix elements (including the hbar/2) could also be added to spin operator. I agree the higher spin matrices should be moved out of the article since they are not "Pauli matrices". Correct me if wrong, but Pauli matrices refers to the spin half case only. M∧Ŝ c2ħε Иτlk 17:40, 12 January 2015 (UTC)
It makes NO SENSE not to have the higher spin matrices described. Even if you are so pedantic to not consider them pauli matrices (in contradiction to many standard texts), they are direct generalizations. For example, if I will google spin matrices, it leads me to this page.
In addition, I can not seem to find ANY link on this page that will take me to the place describing the higher spin matrices. This is absolutely ridiculous. 136.152.38.211 ( talk) 23:19, 13 April 2015 (UTC)
What is the point of having the formula
in the lead? Who uses or remembers it? It seems like it should be deleted, but if others have a good reason it could be kept.
M∧Ŝ
c2ħε
Иτlk
17:47, 12 January 2015 (UTC)
I beg to differ... the first thing that one does is to run to the compact expression and dot to a 3-vector, as detailed in the Pauli-vector section later.. a bit of duplication might not hurt anyone... Will address other discussion later, but L&L is online out there... Cuzkatzimhut ( talk) 18:05, 12 January 2015 (UTC)
[1] by editor Cuzkatzimhut deleting my edit showing the relation between Pauli vectors and the geometric product with the comment "Inappropriate and promotional. At best a footnote in 3.1 or 2.2.)"
What is it in the edit that is promotional? Why is is it inappropriate? How does a "promotional and inappropriate" edit suddenly become an OK edit as long as its a footnote?
I have reverted pending an explanation. Selfstudier ( talk) 17:19, 26 October 2017 (UTC)
In my opinion, the equation is not even wrong but much worse. On the right side of the equal sign there is a vector and on the left side there is a scalar (i.e. a trace value). (unsigned by User:217.95.166.32)
We might have cognitive dissonance here. This is not a forum. If you have an improvement to readability, you may propose it on this page. The notation employed, and explained clearly for the Pauli vector, is universal in the physics community, and often detailed in most textbooks. The quantity in the parenthesis is a matrix. The quantity in the square bracket is a vector with matrix components. The trace of the square bracket is therefore a vector with scalar components, which comports with the right-hand side. The page has 102 watchers/editors, and 25 of them have engaged recently, as you presumably checked from the page info. If you could convince some of them of your improvement, well.... Cuzkatzimhut ( talk) 22:55, 14 November 2018 (UTC)
Ground rules: NO extraneous arcane vanity cites. Proceed to propose concrete phrase substitutes here, not in the article, instead of tendentious philosophical peroration. Cuzkatzimhut ( talk) 19:13, 7 December 2019 (UTC)
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion:
Participate in the deletion discussion at the nomination page. — Community Tech bot ( talk) 03:22, 25 April 2020 (UTC)
Are Pauli matrices (2,0), (1,1), or (0,2)? Just granpa ( talk) 17:33, 2 July 2020 (UTC)
When I open the page on Chrome or Edge, the third Pauli matrix reads [0 i; i 0], instead of [0 -i;i 0]. My version of Google Chrome is 87.0.4280.88 (Official Build) (64-bit) and Microsoft Edge is 87.0.664.66 (Official build) (64-bit). When I open the page on Firefox it looks fine.
Mimigdal ( talk) 09:38, 22 December 2020 (UTC)
Cuzkatzimhut ( talk) 12:16, 22 December 2020 (UTC)
Hermitian and unitary implies involutory. The identity matrix and its opposite are both hermitian unitary and then involutory, but not Pauli. It seems that null trace should be included in the definition of a Pauli matrix. And strip out the involutory condition BatracioVerde ( talk) 12:21, 12 July 2024 (UTC)
![]() | This page is not a forum for general discussion about Pauli matrices. Any such comments may be removed or refactored. Please limit discussion to improvement of this article. You may wish to ask factual questions about Pauli matrices at the Reference desk. |
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||||||||||||
|
![]() | This article links to one or more target anchors that no longer exist.
Please help fix the broken anchors. You can remove this template after fixing the problems. |
Reporting errors |
Somebody should redirect Pauli Gate to go to this page, I have no experience doing this, and it wasn't as easy as #REDIRECT Pauli Gate so I didn't do it.
I removed this:
I don't see in what sense four matrices can "generate" an uncountable group, especially if they aren't even elements of that group. AxelBoldt 00:34 Apr 29, 2003 (UTC)
Looking at the replacement
I think I see the source of my confusion. We are not talking about generators in the sense of group theory, but rather "infinitesimal generators" of a Lie group, i.e. the elements of its Lie algebra. This should be clarified somewhere. So what we are really saying is that σ1,σ2 and σ3 form an R-basis of the Lie algebra su(2) of all Hermitian 2x2 matrices with trace 0, is that correct?
Also, the above link to group representation is misleading, since we are really representing a Lie algebra, not a group. I'll try to weave that into the article. AxelBoldt 20:02 Apr 29, 2003 (UTC)
I think the sign of has been inadvertently flipped. Indeed, I don't know what books y'all are looking at, but it at least some textbooks this guy does appear with the other sign.
Why is the other sign preferable? Self-consistency, but more for aesthetics than anything else. The problem is that with the present sign, multiplying by and exponentiating gives clockwise rotation, whereas give counterclockwise rotation. That's a bit awkward and is a minor annoyance in related articles like Lorentz group. OK, this might be my most pedantic quibble yet, but if anyone agrees the sign needs fixing, please do it (don't forget to check the commutators, which you'll probably also need to modify).--- CH (talk) 16:42, 13 July 2005 (UTC)
At this point, I feel, it may be useful to emphasize the anticommutator relations of the matrices as their defining equations. This clarifies their relationship to the invariant metric tensor defining SO(3) and their role in the corresponding Clifford algebra. This algebraic definition allows for a manifold of alternative representations. Please, have a look at the matrices for an analogy.
You may, of course, insist on etc. to keep conventions of chirality in 3-dimensional space.
Direct calculation shows that the Lie algebra su(2) is the 3 dimensional real algebra spanned by the set {i σj}.
What is meant by a real algebra here? Surely the elements of the set {i σj} are complex. Wiki me ( talk) 22:30, 27 February 2008 (UTC)
I think it may help eliminate confusion to use the normal convention of denoting Lie groups with uppercase letters and their corresponding Lie algebras with lowercase letters. I changed some instances that I noticed in the article. Thanks. Idempotent ( talk) 12:02, 1 August 2008 (UTC)
With regard to Quantum mechanics, would a section on probability of measurement of the electron's spin not be good/informative? —Preceding unsigned comment added by 92.236.96.97 ( talk) 12:25, 2 September 2008 (UTC)
I've tried printing the article as it stands, using four different printers, all of which print other Wikipedia articles OK, but for the Pauli Matrices article I find the Commutation relations (near top of 2nd page, printing as normal A4 in portrait orientation) don't come out, neither do the contents of the "Proof of (1)" box (lower on 2nd page), nor do parts of "Proof of (2)" box; and a single line for p = span{isigma1,isigma2}. Unless others find the printing is AOK, it would be nice if someone could amend this please (I'd rather not mess with it myself). Thanks PaulGEllis ( talk) 20:14, 7 September 2008 (UTC)
As a new reader (despite already knowing clifford algebra) I found the commutator section exceptionally unclear. The Pauli vector was defined, but only by context could one see the mechanism that it provided to relate a vector to a "Pauli vector".
Additionally the statement "(as long as the vectors a and b commute with the pauli matrixes)" was confusing since one doesn't ever directly multiple these R^3 vectors with these 2x2 matrixes.
I've attempted to clarify this, adding in a bit of the reverse engineering context that was required to understand the text. In doing so I've split the Pauli vector definition out of the commutator section.
As somebody who doesn't have any text that covers this material I can't comment on how well used the Pauli vector concept is. If one's aim is to learn how to use the matrix algebra (ie: for things like rotations that aren't even covered in this article), I'd be inclined to define a vector in terms of coordinates directly:
and omit (or defer to an afternote) the Pauli vector entirely.
Peeter.joot ( talk) 05:28, 6 December 2008 (UTC)
Isn't the Pauli algebra just the good ol' real algebra of 2 by 2 complex matrices? It seems worth to mention it, along with the much more exotic reference to the real Clifford algebra 3,0. 147.122.52.70 ( talk) 11:39, 20 April 2009 (UTC)
This article is far from being complete. The Pauli matrices play a big role in Quantum Information wich should be highlighted. This is a big mistake, because Quantum Information is one of the most clearest ways to understand Quantum Mechanics.
This article should have separated sections for the following three topics: 1) Connection of the Pauli matrices with quantum error correcting codes. 2) Information about the generalised Pauli group: pauli matrices can be defined for any finite group (abelian or not). 3) The stabiliser formalism and the Gottesman-Knill theorem! Relation to Clifford operations! — Preceding unsigned comment added by Garrapito ( talk • contribs) 02:22, 18 June 2011 (UTC)
Here it should be mentioned that this is the quantum-mechanics of the simple alternative (eigenvalues +1,-1), i.e. the lowest-dimensional non-trivial quantum-mechanics (in Hilbert-space C2). This was used by Carl-Friedrich von Weizsäcker for his Ur-theory - Urs are the basic two elementary particles in this theory, corresponding to the two inequivalent representations mentioned here. Mathematically - thanks for mentioning the Clifford-algebra here. The Pauli-matrices generate the real, associative Clifford-algebra over an Euclidean R3 (defined by a positive-definite real bilinear-form). There is an alternative on R3 with respect to an indefinite non-degenerate bilinear-form of signature (++-), with a two-dimensional representation by complex 2x2 matrices. These are given by an alternative to the Pauli-matrices, changing some signs. Another mathematical remark: With respect to the canonical bilinear-form trace(AB)-trace(A)trace(B) for matrices A,B ∈ Cn,n (i.e. square matrices), the 4-dimensional real vector-space, spanned by the 2x2 identity-matrix and the three Pauli-matrices is a real Minkowski-space with signature (+---). Sofar there is no physical meaning behind this, it is just „Zufall", like the other one, namely that the only unit-spheres Sn that are Lie-groups are those for n=1 and n=3. Taking the above alternative to the Pauli-matrices, this signature on the four dimensional vector-space becomes (++--). — Preceding unsigned comment added by 130.133.155.70 ( talk) 13:51, 24 September 2012 (UTC)
Thus Fropuff's isomorphism above not only is one of 4-dimensional real vector-spaces, but also one of Minkowski-spaces.
There is another remark above: Certainly there is an equality of this Clifford-algebra to the general linear complex algebra of endomorphisms of C2. The proof even is easy, it suffices to show, that the matrices you get by matrix multiplication are linearly independent. But - this remark also is misleading, since both associative algebras have n-dimensional generalizations, and these are not isomorphic for higher dimensions, for instance in the case of Dirac-matrices. Relativistic physics neads Dirac matrices, which with respect to the above bilinear-form of matrices are a Minkowski-space as well. The same holds for the Duffin-Kemmer-Petiau matrices. So referring to this isomorphism makes sense only for the 2-dimensional case, corresponding to the fact, that simple Lie (and Jordan) algebras of lower dimensions collapse to only a few isomorphism classes.
Let me add, that the Clifford-algebras are universal envelops of a class of Jordan-algebras, defined by the underlying non-degenerate symmetric bilinear-forms in the same way, as the Heisenberg Lie-algebras are defined in terms of symplectic forms. Thus Bose-Einstein and Fermi-Dirac creation and annihilation operators are traced back to the two types of non-degenerate bilinear forms, the symmetric and the skew ones (and therefore there is no third type of statistics).
As the Pauli matrices were developed in the study of spin 1/2 particles, I think the article should have a physics bias. I'd propose that the explanation of their use in physics be moved to be more prominent, and the interpretation of the two-component vectors/spinors be explained. If I understand rightly, each spinor corresponds to a point on the sphere, and is the state of the system with a definite spin in that direction. The components map to the Riemann sphere by dividing one component by the other. Explaining this in the article would explain how to find eigenvectors of linear combinations of Pauli matrices, which is important as these are the observable states for the observables these combinations represent. At the moment, the article only explains the eigenvectors of the Pauli matrices themselves. Count Truthstein ( talk) 17:11, 29 November 2012 (UTC)
I think the problem comes from the fact that there are multiple choices for generators of the Lie algebra su(2). Looking at Special unitary group: n = 2, we see that the algebra is generated by u1, u2 and u3 with [u1,u2] = u3 and cyclic permutations of the indices. The most obvious relation to the Pauli matrices (from the definitions of the matrices in this article, and using their commutation relations) would be to have ui = −i σi. However, as is apparent at the other article, u1 = i σ1,u2 = −i σ2 and u3 = i σ3 works as well, with an unexpected minus sign on the second matrix (the minus sign could of course be on any of the matrices). Count Truthstein ( talk) 17:03, 9 March 2013 (UTC)
An IP made this , and I reverted since there didn't appear to be any problem at all before the indents were removed. it looks odd to have some formulae not indented and pressed against the screen, and the rest indented. Can anyone confirm any technical problems of this nature? Thanks, M∧Ŝ c2ħε Иτlk 07:01, 4 May 2013 (UTC)
Shouldn't the lead section be shorter? -- Mortense ( talk) 11:32, 27 December 2014 (UTC)
How about moving the higher spin matrices, without the ħ, of course, to Rotation group SO(3)#A note on representations? Higher spins hardly belong here. Concerning the arbitrary j case commented out, how about indexing a from 1 to 2j+1, as the novice would expect, in which case Jz = (j+1−a) δb,a, and the J± added and subtracted to have Jx and Jy, which are more familiar? E.g., Jx = (δb,a+1+δb+1,a) √(j+1)(a+b−1)−ab /2, which agrees with the examples. I don't presume to foist work orders on the commentor, though... Cuzkatzimhut ( talk) 17:03, 9 January 2015 (UTC)
The higher-spin matrix elements (including the hbar/2) could also be added to spin operator. I agree the higher spin matrices should be moved out of the article since they are not "Pauli matrices". Correct me if wrong, but Pauli matrices refers to the spin half case only. M∧Ŝ c2ħε Иτlk 17:40, 12 January 2015 (UTC)
It makes NO SENSE not to have the higher spin matrices described. Even if you are so pedantic to not consider them pauli matrices (in contradiction to many standard texts), they are direct generalizations. For example, if I will google spin matrices, it leads me to this page.
In addition, I can not seem to find ANY link on this page that will take me to the place describing the higher spin matrices. This is absolutely ridiculous. 136.152.38.211 ( talk) 23:19, 13 April 2015 (UTC)
What is the point of having the formula
in the lead? Who uses or remembers it? It seems like it should be deleted, but if others have a good reason it could be kept.
M∧Ŝ
c2ħε
Иτlk
17:47, 12 January 2015 (UTC)
I beg to differ... the first thing that one does is to run to the compact expression and dot to a 3-vector, as detailed in the Pauli-vector section later.. a bit of duplication might not hurt anyone... Will address other discussion later, but L&L is online out there... Cuzkatzimhut ( talk) 18:05, 12 January 2015 (UTC)
[1] by editor Cuzkatzimhut deleting my edit showing the relation between Pauli vectors and the geometric product with the comment "Inappropriate and promotional. At best a footnote in 3.1 or 2.2.)"
What is it in the edit that is promotional? Why is is it inappropriate? How does a "promotional and inappropriate" edit suddenly become an OK edit as long as its a footnote?
I have reverted pending an explanation. Selfstudier ( talk) 17:19, 26 October 2017 (UTC)
In my opinion, the equation is not even wrong but much worse. On the right side of the equal sign there is a vector and on the left side there is a scalar (i.e. a trace value). (unsigned by User:217.95.166.32)
We might have cognitive dissonance here. This is not a forum. If you have an improvement to readability, you may propose it on this page. The notation employed, and explained clearly for the Pauli vector, is universal in the physics community, and often detailed in most textbooks. The quantity in the parenthesis is a matrix. The quantity in the square bracket is a vector with matrix components. The trace of the square bracket is therefore a vector with scalar components, which comports with the right-hand side. The page has 102 watchers/editors, and 25 of them have engaged recently, as you presumably checked from the page info. If you could convince some of them of your improvement, well.... Cuzkatzimhut ( talk) 22:55, 14 November 2018 (UTC)
Ground rules: NO extraneous arcane vanity cites. Proceed to propose concrete phrase substitutes here, not in the article, instead of tendentious philosophical peroration. Cuzkatzimhut ( talk) 19:13, 7 December 2019 (UTC)
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion:
Participate in the deletion discussion at the nomination page. — Community Tech bot ( talk) 03:22, 25 April 2020 (UTC)
Are Pauli matrices (2,0), (1,1), or (0,2)? Just granpa ( talk) 17:33, 2 July 2020 (UTC)
When I open the page on Chrome or Edge, the third Pauli matrix reads [0 i; i 0], instead of [0 -i;i 0]. My version of Google Chrome is 87.0.4280.88 (Official Build) (64-bit) and Microsoft Edge is 87.0.664.66 (Official build) (64-bit). When I open the page on Firefox it looks fine.
Mimigdal ( talk) 09:38, 22 December 2020 (UTC)
Cuzkatzimhut ( talk) 12:16, 22 December 2020 (UTC)
Hermitian and unitary implies involutory. The identity matrix and its opposite are both hermitian unitary and then involutory, but not Pauli. It seems that null trace should be included in the definition of a Pauli matrix. And strip out the involutory condition BatracioVerde ( talk) 12:21, 12 July 2024 (UTC)