Talk:Gamma matrices

message: I fixed a sign on the chiral definition, as the text said that \gamma^i stays the same, as does my book... —The preceding unsigned comment was added by 131.111.225.229 (talk • contribs) 22:31, 12 January 2007  (UTC)
The sign convention here apparently follows Peskin and Schroeder, but they warn that other books may use different sign conventions...
Can someone name a book that uses \gamma ^0 = \begin{bmatrix} 0 & -I \\ -I & 0 \end{bmatrix}, \vec{\gamma} = \begin{bmatrix} 0 & \vec{\sigma} \\ -\vec{\sigma} & 0 \end{bmatrix}, \gamma ^5 = \begin{bmatrix} I & 0 \\ 0 & -I \end{bmatrix} ?
It might be worth mentioning in the text. --Immer in Bewegung (talk) 05:45, 8 September 2008 (UTC)
replies: text: Kaku, QFT, uses the above convention. (Michio Kaku, Quantum Field Theory, , appendix A)--Michael C. Price talk 10:16, 9 October 2009 (UTC)
replies: text: Itzykson & Zuber appendix A. The article now covers both chiral conventions. 67.198.37.16 (talk) 05:23, 24 November 2020 (UTC)
thread_title: Chiral definition

message: I dislike the "one possible representation [...] is" at the top, especially given that it doesn't seem to match any of the representations described below - it's the Dirac representation with a sign change for \gamma^1 and \gamma^3? I'd much rather have an explicit statement of the representation, but since I can't figure out why the signs are what they are, I don't want to edit...
Themel (talk) 21:05, 22 November 2007 (UTC)
thread_title:  Expansion at the top 

message: The edits made by the two anons since the beginning of February 2008, although undoubtedly done in good faith, do not improve the article. In my view, they obscure its meaning with attempts at spurious rigour, making the article less transparent. An explanation has been asked for but has not been forthcoming. Accordingly I have reverted to the version of 1 February. If I have reverted any useful edits, I apologise. Xxanthippe (talk) 23:40, 17 February 2008 (UTC)
thread_title: Anons reverted

message: This might be a silly question because I'm just a layman. Why are the matrices not in row echelon form? -Craig Pemberton 08:20, 26 December 2009 (UTC)
replies: text: Because the place of the rows is important. Switching the rows will change the physics. you don't just put matrices in "row echelon form" for pleasure. Setreset (talk) 10:26, 26 December 2009 (UTC)
thread_title:  Row echelon form 

message: Doesn't it make sense to add a Dirac-Pauli representation, as it seem to be the default representation? See the book "The Dirac Equation" of Thaller on page35 for instance ().  — Preceding unsigned comment added by 93.104.36.169 (talk) 21:38, 20 September 2011 (UTC)
thread_title:  Dirac-Pauli representation 

message: Hi
The equation \displaystyle\gamma^\mu=(\gamma^0,\gamma^1,\gamma^2,\gamma^3) = \gamma^0 e^0 + \gamma^1 e^1 + \gamma^2 e^2 + \gamma^3 e^3 appearing in the section "Physical Structure" is just nonsense. It's not "misleading" as is pointed out later, it's nonsense. Why not just write like this:
The 4-touple (\displaystyle\gamma^\mu)=(\gamma^0,\gamma^1,\gamma^2,\gamma^3) is often loosely described as a 4-vector. But ...
One of the virtues of the Einstein notation is that nonsense equations tend to reveal themselves directly;) YohanN7 (talk) 10:32, 11 September 2012 (UTC)
replies: text: So, I finally rewrote it (completely). The title "Physical structure" hints more than that only LT properties should go in. But this is what was there before, and this is what is there now, hopefully better presented. YohanN7 (talk) 18:49, 2 November 2013 (UTC)
thread_title:  Physical Structure 

message: So far have shown for two cases, 1 and 3. Need to extend to general odd number (if I could I would)...
Hai2410 (talk) 00:18, 30 January 2013 (UTC)
thread_title:  Incomplete proof "trace of any product of an odd number of gamma matrices is zero" 

message: Why there is no proof nor reference to source for misc property 5?  — Preceding unsigned comment added by 186.137.53.184 (talk) 03:19, 20 September 2013 (UTC)
replies: text: Why not write one yourself? Xxanthippe (talk) 04:43, 20 September 2013 (UTC)
thread_title:  Miscelaneous property 5 (proof lacking) 

message: The following from the lead needs reformulation:
:When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of spacetime acts. This in turn makes it possible to represent infinitesimal spatial rotations and Lorentz boosts.
It is true when taken with a grain of salt and in reverse order. It would be better to note that the generators of the Lorentz group has a spin representation expressible in terms of the gammas as presented in Gamma matrices#Physical structure. Applying this representation to an arbitrary 4-dimensional vector space yields a space of spinors. (The covariance/contravariance needs no mention, it will only add confusion.)
I'd appreciate if somebody could help me formulate this in good lead lingo. YohanN7 (talk) 14:02, 6 November 2013 (UTC)
thread_title:  The lead 

message: In all the Quantum Field Theory textbooks I've checked, including Schwartz's Quantum Field Theory and the Standard Model, Zee's Quantum Field Theory in a Nutshell, and Weinberg's Quantum Theory of Fields, it says that
\gamma^0 = \left(\begin{matrix}0&0&1&0\\0&0&0&1\\1&0&0&0\\0&1&0&0\end{matrix}\right)
in the Dirac representation. But this does not match the value given at the beginning of this article! Is the value of \gamma^0 wrong here?
Thanks,
Gneisss (talk) 07:09, 30 October 2018 (UTC)
replies: text: I figured it out -- all of these books were using the Weyl representation. Gneisss (talk) 23:51, 11 November 2018 (UTC)
replies: text: The Dirac representation is nice, if one is learning about antiparticles for the first time, and nifty things like zitterbewegung. Once you settle in, the Dirac representation mostly just gets in your way, because you realize that left-right is what's important, not particle-antiparticle. It would seem that the newer books are apparently just dumping the older Dirac representation as not being very useful. Thus, the march of progress. I would add this to the article, except I can't figure out how to say it in an encyclopaedic tone.   67.198.37.16 (talk) 06:01, 24 November 2020 (UTC)
thread_title:  Is <math>\gamma^0</math> wrong? 

message: The article states the following about the Majorana representation: `The reason for making all gamma matrices imaginary is solely to obtain the particle physics metric (+, −, −, −) in which squared masses are positive'.
I do not find this to be very enlightening, since an observable like a squared mass is always positive. 2001:638:504:C07C:CDE7:3AF3:25C9:FC88 (talk) 11:21, 4 June 2019 (UTC)
replies: text: A squared mass here should be taken to mean "the squared norm of a 4-momentum", which may indeed be negative depending on convention. Linkhyrule5 (talk) 13:28, 9 April 2023 (UTC)
thread_title:  Squared mass 

message: I would like to add a citation section.  This makes it easier for the reader, a citation section for citations and a reference section for references.  Is there any objection or concerns? TMM53 (talk) 06:28, 15 January 2024 (UTC)
thread_title:  Add a citation section