Talk:Parity (physics)

Conservation of parity
I redirected conservation of parity here because it is discussed in the article, but it would be good to increase its visibility. -- Kjkolb 07:35, 25 November 2005 (UTC)

Fixing the global symmetries
How could it be, then if F=B+L, and if B=L=0 for Majorana neutrinos, then F=1 ?


 * This is the point. So far, every particle that we've found has obeyed F=B+L.  No one knows why, it's just an observation.  It is an open question whether Majorana neutrinos exist, but if they do, they would break the F=B+L rule.  Which isn't good or bad, it's just a fact, and it means that parity might have eigenvalues other than plus or minus one. JarahE 22:22, 27 April 2006 (UTC)


 * But P^2 = 1 implies P can only have eigenvalues that square to 1...
 * Shambolic Entity 02:01, 25 January 2007 (UTC)


 * OK, then I understand if F=B+L is empirical.Hidaspal 19:22, 29 April 2006 (UTC)


 * Yeah, not only is it empirical, but there may even be a counter-example if Neutrino's really turn out to have Majorana masses as people seem to suspect now adays. This argument is very old, I think it's Steven Weinberg's from maybe 40 years ago, before there was evidence for Majorana neutrinos.JarahE 15:01, 2 May 2006 (UTC)

Why Q (electric charge) is mentioned as a charge of a global symmetry group?


 * The Lagrangian of electromagnetism is invariant under the rotatation of the wavefunction of each charge Q particle by e^{ialpha Q} for any alpha. In the particular case in which alpha is constant, this is a global symmetry.  You might want to look at the page Noether's theorem which explains this phenomenon in more generality.  To my knowledge, all conserved charges in quantum field theory, not just electric charge, arise similarly.  JarahE 22:22, 27 April 2006 (UTC)


 * My point is the following. Electric charge is related to a local gauge symmetry. Of course you can always say, that say alpha(x) = beta(x) + c, but is it possible then assign c again to "another" or "assign again" to the electric charge? It sounds that you can then multiply the number of symmetries arbitrarily. Or do you say here, that for the momnet lets ignore the local symmetries, because the global part is enough for this issue? It seems you are saying this latter case. Hidaspal 19:22, 29 April 2006 (UTC)


 * Your formula makes it look like the global symmetry is just some Fourier mode of the local symmetry, but physically there's a big difference. In a path integral you fix boundary conditions, which means that global symmetries are fixed and local symmetries are integrated over.  In examples this seems to mean that local gauge symmetries are just redundancies of the description, where as global symmetries really change your state, i.e. they change the observables.  Gauge symmetries in particular have to leave the boundary conditions fixed, so the zero mode of your alpha(x) is not a gauge symmetry.  So anyway it seems to me like for noncompact spaces there's no arbitrariness in separating out the global symmetries (although you can always add a local symmetry to a global one and get another representative of the same global symmetry), the constant rotation corresponds to a real physical transformation. JarahE 15:01, 2 May 2006 (UTC)

Hidaspal 21:13, 27 April 2006 (UTC)

Simple symmetry relations
"In a quantum theory states in a Hilbert space do not need to transform under representations of the group of rotations, but only under projective representations." - it sounds like a restriction though there is an extension in reality from representations of O(3) to SU(2). Projective to what? There are a lot of missing statements, which makes the whole thing unclear and ununderstandable. Hidaspal 21:30, 27 April 2006 (UTC)


 * Your appraisal sounds a bit extreme, but anyway, I also think that the term projective representation is misleading because it sounds like a kind of representation. This leads to your observation that the phrase sounds like a restriction.  Instead the opposite is true, a representation is a kind of projective representation.  Anyway, I've tried to explain this a bit better.  In particular, I've added the fact that the projection is with respect to the overall U(1) phase of a state in the Hilbert space, as rotations of a Hilbert space vector by an overall phase do not change the corresponding physical state.  Do you understand it now?JarahE 22:35, 27 April 2006 (UTC)


 * Sorry for being extreme.:-) No, I do not understand, but the basic problem, that I have only learned another approach, which is probably identical, but does not mention projective representation at all. My book "HF Jones, 1990" does not do that. The picture in my mind is that we start from SO(3) which is a Lie-group, then realize, that it has the same Lie-algebra than SU(2) and it allows reprezentations of SU(2) which are not reprezentations of SO(3), but for us the Lie-algebra is important (the same handwaving as "use projective instead of real representation") not the group, and if the Lie-algebra allows, then spin-half will occur, etc.


 * So I understand that only means extension. But I do not know yet, whether my picture is the same as the "projective representation picture". I think you might be more specific, and less abstract, then more of us will understand. Mention specific groups, the world is specific anyway, we have O(3) rotations and SU(2)-spins :-) Or the best, if you do it twice, once beeing abstract, and mathematically more correct, and once more specific and more understandable for many. Sorry again for beeing extreme. Hidaspal 20:46, 29 April 2006 (UTC)


 * The two specific groups, in the case of massive particles are SO(N) and Spin(N), which in 3+1 dimensions means that the little group of the rotation group is SO(3) and the projective representations of SO(3) are the ordinary representations of its universal cover SU(2). It so happens that SO(3) and SU(2) have the same algebra, which many books use as a pretext for why fermions transform under a rep of SU(2) that is not a rep of SO(3).  But this argument is too fast, because in classical physics for example states transform as reps of SO(3), ie there are no fermions. The fact that quantum states only need to be reps of SU(2) and not of SO(3) is really a quantum effect, its a result of the choice of phase in a vector in the Hilbert space.


 * The standard argument that you cite fails in general, as not all projective reps are reps of groups that have the same algebra, more generally they are reps of groups that have an algebra that has one extra generator (called a central extension). This is occurs for example in the Wess-Zumino-Witten model, the classical symmetry is a loop group but the states transform under projective reps of the loop group, which are affine Lie algebras.  The argument that you cite always works when there is only a discrete set of possible phases to choose (like the plus or minus one in the choice of fermions and bosons).


 * So anyway, for the page, your suggestion is to mention the specific groups SO(3) and SU(2) or SO(N) and Spin(N) as examples? JarahE 15:09, 2 May 2006 (UTC)


 * Yes Hidaspal 23:14, 6 May 2006 (UTC)

It is written "'Quantum theory predicts that states in a Hilbert space do not need to transform under representations of the group of rotations, but only under projective representations. The word projective refers to the fact that if one projects out the phase of each state, where we recall that the overall phase of a quantum state is not observable, then a projective representation reduces to an ordinary representation. All representations are also projective representations, but the converse is not true, therefore the projective representation condition on quantum states is weaker than the representation condition on classical states.'" But if representations form a strict subclass of projective representations, shouldn't the projective representation condition be a stronger one than the representation not make sense, and also, doesn't the "do not need...but only" construction in the first sentence not make sense? I think I am implicitly assuming that phrases like "transforms under representations of the group of rotations" mean "transforms under all such representations". I may be wrong about this, and, if so, would like to be corrected, but if some other interpretation is needed, perhaps the article should be rewritten to be made clearer. Nwalton125 (talk) 19:33, 3 July 2022 (UTC)

Contradiction in intro
The first line states "...a parity transformation is the simultaneous flip in the sign of all spatial coordinates." Almost directly below this it is stated that "In a two-dimensional plane, parity is not the same as a rotation by 180 degrees." These two statements blatantly contradict each other. Shambolic Entity 02:01, 25 January 2007 (UTC)


 * The first statement is about the three-dimensional world in which we live and is much more important than the second statement which is about a two-dimensional imaginary world. Since the context is different, they do not contradict each other. JRSpriggs 09:55, 25 January 2007 (UTC)


 * There is one definition that fits both: "Parity is a flip in the sign of one spatial coordinate." This works for 3D as well as 2D cases as well as in arbitrary dimensions. The definition given in the first sentence only works in odd number of dimensions (You can think of x, y, and z flips as 3 parity transformations that form again a parity transformation. In two dimensions, flipping x and y brings you back to the original parity). --149.217.1.6 (talk) 16:28, 29 April 2008 (UTC)


 * I just changed the introductory sentence. I don't understand why the three-dimensional definition is taken with such importance, and later reflection is introduced as being something independent from parity that has to be combined with rotation to form parity...?!? Reflection CHANGES the parity. Parity says something about the handedness of objects in space-time. If you transform an object through a reflection, in general you can not bring it back into the original position just by a rotation, so reflection IS a parity transformation. On top of that, reflection as a definition for parity works in all space dimension. The definition of flipping the signs of ALL coordinates is IMHO a simplified definition that only works in odd number of dimensions. Really you perform 3 parity transformations in a row, which is why you end up with something that you could have obtained by a single (reflection) parity transformation. I think the paragraph about reflection and so on needs to be re-written. Do people agree? --149.217.1.6 (talk) 16:46, 29 April 2008 (UTC)


 * I agree the introduction is contradictory the way it is written. The contradiction I see (which may have been added later), says something like "The determinant (in ANY number of dimensions) is -1 for a parity change, but +1 for a rotation.  In 2 dimensions, negating both X and Y is NOT a parity change, but a rotation".  This is a contradiction with the previous mentioned "flipping all signs is a parity change"... I mean if you flip all signs in two dimensions, then it will be a parity change... but the quote I just gave said it is not a parity change... but the quote also said it works for ANY number of dimensions... how can there be an exception for 2 dimensions?

Well if you calculate the determinant for a 2d matrix with ((-1,0),(0,-1)) then you get +1 (rotation) which is consistent with the text I just quoted (both the ANY dimensions part, and the 2D example part). However it is still inconsistent with what everyone is talking about here: simply flipping the sign of all coordinates does not (always) work. And because we shouldn't expect the average reader to be able to calculate N-dimensional determinants in their head, this is just a mass of confusion.

I think the solution is to write early in the intro what another suggested before; that a parity transform occurs when you negate an odd number of elements, in any dimension; and perhaps point out that for 3 dimensions, this is the same as negating all coordinates. And perhaps also clarify (later in the intro, where my quote came from) that negating all coordinates in 2 dimensions is not parity change because it is not an odd number of elements being negated. But that seems it might be confusing too... I guess I would try editing the page right now, if I were an expert or had a reliable source... opinions ? Hydradix (talk) 03:17, 2 August 2016 (UTC)

Intrinsic parity
This article could really use a definition of instrinsic parity. I would do it myself but, since that is the topic I came here to learn about, I don't know the definition myself. Tpellman (talk) 17:22, 29 April 2008 (UTC)

Neutral Pion Decay
Although the neutral pion decay at the bottom of the article is indeed electromagnetic, and parity is conserved, the interaction still INVOLVES the weak interaction - the Standard Model plonks a virtual kaon in there, which of course arises from weak decay. Would it not be better to replace this with, e.g., rho decay to pions or something? Of course, there are always going to be virtual weak interactions integrated over for any process but with the neutral pion interaction it's actually always there. If no complaints, I'll change it. —Preceding unsigned comment added by 41.145.40.166 (talk) 19:11, 1 October 2009 (UTC)

Some questions on parity symmetry
The article mentions that parity symmetry is 'maximally' violated by the weak force. Does the standard model lagrangian itself violate parity symmetry, or is it somehow due to the spontaneously broken symmetry that gives the vacuum a non-zero higgs expectation value?

Also, since CPT is (required?) a symmetry of particle physics, then parity symmetry violation implies time reversal symmetry violation in a very specific way. This seems weird to me. Can someone comment on this in the article? It seems very interesting.

Looking at the definition of an inertial frame in wikipedia, a parity transformation would yield another inertial coordinate system. Since SR requires physics to be the same in all inertial coordinate systems, yet experiments show there is not parity symmetry in weak decays, either the inertial frame article, or the special relativity article, or this article on parity needs to be updated. Otherwise wikipedia seems to imply that experiments on parity disprove special relativity.

130.126.14.198 (talk) 08:11, 26 January 2010 (UTC)

Brookhaven collider violation
An NYT article was published yesterday that discusses a brief parity violation observed at the Brookhaven collider. This should be added, and the article can be found here: http://www.nytimes.com/2010/02/16/science/16quark.html?th&emc=th 68.231.22.246 (talk) 16:18, 16 February 2010 (UTC)


 * For a less sensationalistic headline, the BNL page itself might be a good place for information: http://www.bnl.gov/rhic/inside/news.asp?a=1588&t=today If I'm reading that first paragraph correctly, local violations were already predicted by QCD, and this is just the first observation of that. Gmalivuk (talk) 20:40, 8 May 2010 (UTC)

The definition of parity
This is clearly one of a group of related articles including T-symmetry, C-symmetry and C-Parity. The naming as Parity is unhelpful, seeming to suggest that the other ideas are somehow subordinate to this idea. There is clearly some overriding idea to which these articles contribute, but it is not clear what this idea is. I would guess they all address some aspect of the question of invariance of the laws on physics under various transformations. As I am a novice trying to learn the subject, indication of this would help.

Turning to this particular article:

There is no explanation of why parity is relevant. Symmetry relations are the first topic after the introduction with no explanation as to why.

The statement “In physics parity relates to the sign of a spatial coordinate” can only apply to P-parity. It cannot apply to parity in physics in general.

The article does not define the values that parity can take, although by implication they seem to be +1 and -1. How to calculate parity in some particular circumstance is not defined. If I have an n-dimensional spatial vector containing both positive and negative terms, what is its parity? There is some discussion of the determinant of transformation matrices in 2 and 3 dimensions with value +1 and -1 relating to reflection and rotation. The article does not say whether the value of the determinant in some way defines parity.

Confusingly, having defined parity by ‘sign’, the section ‘Effect of spatial inversion on some variables of classical physics’ classifies variables according to odd and even parity (which is the mathematical concept of parity). The related T-symmetry and C-symmetry articles also refer to even/odd parity.

The article specifies an operation, ‘inversion’, as the ‘flip’ of the sign of a spatial coordinate. Is this formally the reflection in that axis? The other symmetry/parity articles variously use ‘conjugate’ and ‘reversal’ to describe the ‘flip of the sign’; this is unhelpful. Parity inversion is given the confusing synonym ‘parity transformation’ as if there was no other possible transformation of parity.

In example considering three dimensions:
 * $$V_x: \begin{pmatrix}x\\y\\z\end{pmatrix} \mapsto \begin{pmatrix}-x\\y\\z\end{pmatrix},$$

might better be written as


 * $$P_x: \begin{pmatrix}x\\y\\z\end{pmatrix} \mapsto \begin{pmatrix}-x\\y\\z\end{pmatrix},$$

Albear-And (talk) 05:45, 17 February 2010 (UTC)

Article is Only Understandable to Mathematicians and Physicists
Wikipedia is a public use encyclopedia and wherever possible, should include descriptions understandable to the general public (non-scientist lay persons). Scientific language and formulas may be included, but should be in parallel to common-language explanations so that non-scientist readers can understand as much of Wikipedia as possible.

Remember that the main purpose of encyclopedia's in general (and Wikipedia in particular) is to educate and uplift the average reader-- not to to talk in a secretive code between members of a scientific "in-crowd". Science journals are for that, and also serve a valuable purpose, but encyclopedias have a different purpose.

Sean7phil (talk) 17:17, 31 March 2010 (UTC)


 * We're all aware of that. If you have an idea of how to make this more accessible to the lay reader, feel free to edit the article. Headbomb {talk / contribs / physics / books} 19:43, 31 March 2010 (UTC)

Parity in Atomic and Molecular Optics
There should be a section on parity in atomic and molecular optics. Parity provides one of the primary selection rules for determining optical transitions in atomic and simple molecular species. In the dipole approximation, transitions between different electronic states are mediated by the electric dipole operator, which has negative parity. Therefore non-vanishing transition amplitudes are only possible between states of opposite parity for single photon absorption, and between states of the same parity for two-photon absorption. As optical absorption spectroscopy can only detect transitions between states of opposite parity, other means are needed to complete the entire energy spectrum comprising states with the same parity as the ground state. —Preceding unsigned comment added by 130.102.172.3 (talk) 01:48, 3 June 2010 (UTC)

confused references
"Then, combining them with rotations (or successively performing x-, y-, and z-reflections) one can recover the particular parity transformation defined earlier. The first parity transformation given does not work in an even number of dimensions, though, because it results in a positive determinant. In odd number of dimensions only the latter example of a parity transformation (or any reflection of an odd number of coordinates) can be used."

"..defined earlier." "The first parity transform..." "the latter example" These seem to be needed to be updated, since the first paragraph was changed. Unless I'm confused. Or just eliminate unneeded verbiage. GangofOne (talk) 04:12, 18 July 2012 (UTC)

typo, but what's it 'spose to be?
"and so we can choose to call P our parity operator instead of P." I leave for someone else to fix. GangofOne (talk) 04:12, 18 July 2012 (UTC)

Article intro doesn't explain its topic
The article is on parity (in physics); the intro starts by defining what a parity transformation is.

Parity inversion may be important information within the topic, but it isn't the topic itself. Can someone ensure the intro explains its topic? FT2 (Talk 12:29, 11 March 2013 (UTC)

Even/Odd and ±1
The article introduction begins by talking about a transformation which changes parity (determinant -1) or does not (in particular, rotation has determinant of +1). The next section (Simple symmetry relations) also uses similar equations/relations (like P=1 and P=-1)... but this is confusing in regards to the introduction...

Worse, the article then switches to discussing parity in terms of Even and Odd. There is no explanation how even and odd relate to +1 and -1. I'm guessing this has to do with the expression (-1)n ? Such that, if n is even then the result is +1 (no parity change / achiral), and if n is odd then the result is -1 (parity change / chiral). That's what I'm thinking, but don't have a source to confirm my theory. Does anybody know for sure? Hydradix (talk) 06:29, 2 August 2016 (UTC)


 * I have now added definitions of the terms even and odd when first used, with sources plus a link to the math article Even and odd functions. The linked article explains the origin of the term this way: They are named for the parity of the powers of the power functions which satisfy each condition: the function f(x) = xn is an even function if n is an even integer, and it is an odd function if n is an odd integer. So x3 is an odd function because 3 is an odd number. Sounds reasonable though no actual source is given. Dirac66 (talk) 02:34, 26 April 2018 (UTC)

Measurement of parity violation in electron–quark scattering


Is this measurement notable to be mentioned in Parity (physics)? --HNAKXR (talk) 08:28, 10 February 2014 (UTC)


 * If you can phrase it in such a way as to explain why it's notable... sure. I dunno, perhaps it is the first to measure weak currents in electron-quark scattering? Thereby directly validating that, I dunno, W couples to electrons in the S-plane or something like that? What makes this distinctly notable from earlier experiments? 67.198.37.16 (talk) 23:08, 4 December 2020 (UTC)

Reverting own edit: Sister link to Wikiversity
I am removing my own sister link to a Wikiversity article that I wrote. For the record, the link was to Wikiversity:Special:Permalink/1571843, but the actual page is now blanked. I am beginning to realize that instead of proving that this was the proper state associated with two photon decay of even parity, I simply wrote it down. At issue is whether I prove uniqueness of the solution that I wrote down. I will eventually write something in that page, because I did prove that the entangled state does have the proper parity, but without a uniqueness proof it has little value.--Guy vandegrift (talk) 19:04, 24 May 2016 (UTC)

Proposed merge of (−1)F into Parity (physics)
As per discussion at AfD. See Articles for deletion/(−1)F for details ~ Amkgp  💬  19:59, 29 October 2020 (UTC)


 * Balderdash. The fermion number operator has approximately nothing at all to do with parity. Why do you think it does? Yes, OK, this article mentions (−1)F but it does so in a rather complex situation involving Majorana spinors (which is an article I am trying hard to expand). A good place to merge would be to particle number. There should also get a redirect from fermion particle number and if you wanted to get very fancy, then you would mention the chiral anomaly in that article. Which is partly what the Weinberg comments in this article are about (from what I can tell). ...Err, on closer examination, particle number talks about air quality, so is an inappropriate target. Perhaps then particle number operator (which is currently brutish, short and stubby) can be renamed to particle number (quantum mechanics) and given a proper lede. 67.198.37.16 (talk) 22:57, 4 December 2020 (UTC)