Talk:Scalar field

discussion at Wikipedia talk:WikiProject Mathematics/related articles

This article is part of a series of closely related articles for which I would like to clarify the interrelations. Please contribute your ideas at Wikipedia talk:WikiProject Mathematics/related articles. --MarSch 14:10, 12 Jun 2005 (UTC)

new page

I've started a page on Scalar field theory, which no longer just redirects to scalar field. I've done quite a bit myself, but any help from other physicists would be useful and appreciated.--Jpod2 11:15, 19 September 2006 (UTC)[reply]

Why real numbers?

This article directly requires that a scalar field be real-valued and be from a space with real-valued coordinates (Rⁿ → R). However, that seems to neglect complex-valued fields and complex coordinates (Rⁿ → C or Cⁿ → C), which of course can be thought of simply as a different representation, but is nevertheless common. Hpa (talk) 19:45, 30 August 2008 (UTC)[reply]

Impenetrable to the layman

I am not the person who posted the above--I'm not even sure where I should be posting this. I am a random layman who has been poking around Wikipedia's pages on the Higgs boson, gauge theory, quantum field theory, etc., in an effort to understand the LHC... and been completely baffled. I understand that physics can only be simplified so much, but I would appreciate it if any experts would go over those pages (and this one!) and elaborate the definitions, i.e. add longer explanations with smaller words to the compact explanations already there. —Preceding unsigned comment added by 75.153.170.206 (talk) 16:03, 10 September 2008 (UTC)[reply]

As an example, why should anyone be expected to understand how this sentence is relevant to the article?:

In mathematics, or more specifically, differential geometry, the set of functions defined on a manifold define the commutative ring of functions.

LokiClock (talk) 21:11, 8 April 2009 (UTC)[reply]

Time for deletion?

Given that the page Scalar Field Theory now exists and is far more comprehensive, this page simply appears to be redundant. The topic is identical, and handled much better on the other page. Could this page be deleted to avoid confusion? Dusty14 (talk) 16:59, 15 May 2010 (UTC)[reply]

some updates

Given that the article has not yet been deleted (though I think it ought to be), I have at least clarified some of its statements. I think the entire section on scalars in gravity should be removed, if the article isn't otherwise. It is too technical, describes topics that are not really related to scalar fields in general, and should be kept only if it can be boiled down to one sentence. It would be better to put into a more topical page relating to gravity. I removed the comment on continuity, because in most cases I am aware of, some important solutions are distributions, not continuous at all. I also added comments to clarify what it means to be a scalar, since there is a symmetry requirement. In spite of my opinions on the gravity section, I couldn't resist adding a line to it on dilatons in string theory. —Preceding unsigned comment added by Dusty14 (talk • contribs) 17:42, 15 May 2010 (UTC)[reply]

Discussion on new lead image

I reverted an edit to include a new lead image here. My edit was subsequently reverted by the same editor who added it (much contrary to WP:BRD and WP:CON). I have posted to WT:WPM to get further input on the suitability of this image. Sławomir Biały (talk) 20:06, 13 June 2010 (UTC)[reply]

The same image is used in the related Vector field and Tensor field articles. The image compares the fields. For consistency the image should therefore be included in all, or excluded in all - and if the latter then a good reason must be given for exclusion. JohnArmagh (talk) 20:32, 13 June 2010 (UTC)[reply]

"Ordinary" scalars vs scalar densities, etc.

Wikipedia's articles about scalars seems to have a major flaw. Scalars come in a variety of types (and also tensors) depending on how they transform under a coordinate transformation. In general a scalar field of weight $w$ is a scalar field (i.e., no free index object), $f$ , that transforms as ${\bar {f}}({\bar {x}}^{j})=J^{w}f(x^{i})$ , where $J$ is the Jacobian determinant. Here $w$ is an integer. There are two "important" cases, $w=0$ and $w=1$ , which can be termed "ordinary scalars" and "scalar densities", respectively. The distinction is important because the integral of an "ordinary scalar" is not an invariant but the integral of a "scalar density" is. (Lovelock and Rund's book is a good source for the background here.) Physically, temperature and pressure are "ordinary" scalar fields while wave functions and probability densities are scalar densities. Wikipedia seems not to have considered the case of scalars with $w\neq {}0$ and inconsistencies seem to abound. I started a page for scalar density but it needs a lot more work. The semantics of what is meant by "integrating over a region" become very important when discussing these new types of scalars. It's also very easy to get confused where factors of the Jacobian belong. I'll look forward to comments and slowly I'll help remedy this issue. Jason Quinn (talk) 23:38, 22 April 2011 (UTC)[reply]

Spinor fields

Given that this article is very relevant to the field (ho ho ho) of QFT, surely under the 'other kinds of field' section its worth mentioning spinor field, the most famous example of which is of course the Dirac spinor? Just a thought. — Preceding unsigned comment added by 86.149.164.141 (talk) 00:00, 10 July 2014 (UTC)[reply]

Terminology

A gentle nudge regarding terminology. The sentence "Scalar fields are contrasted with other physical quantities..." suggests 'scalar fields' are physical quantities. This is a little like saying vectors are physical quantities, or even that "velocity is a vector". Technically speaking one is a mathematical notion and the other is a physical quantity, and so it would be more correct to say that velocity behaves as a vector, or can be modelled using a vector. 159.134.104.55 (talk) 17:32, 1 June 2015 (UTC)[reply]

Second definition/sense: a field of scalars

At the moment, the article only describes "scalar fields" in the sense of a scalar-valued function over a region. However, in linear algebra, there is another sense of "scalar field" which refers to a field of scalars, where field refers to a the algebraic structure. This is used, for example, on the Vector_space page:

When the scalar field $F$ is the real numbers $R$ , the vector space is called a real vector space. When the scalar field is the complex numbers $C$ , the vector space is called a complex vector space

This second sense is also acknowledged on the Wiktionary and ProofWiki pages for "scalar field."

Should the sense in linear algebra be introduced on this page as well? Or should a disambiguation statement be given that directs to Field_(mathematics)? (A scalar field in this sense is negligibly different from Field_(mathematics) and mostly serves to distinguish from vectors, etc., and thus would not warrant its own page.). Linear_function might be a good template for this. Hukito-san (talk) 05:48, 24 August 2019 (UTC)[reply]

Apparent contradiction

@Quondum (Re: removed link from Higgs boson article) I think it got a bit confused, sorry. I think given the Higgs field is scalar, though,the scalar field article is slightly inaccurate -- the Higgs field has four components and therefore cannot be described as a single number, but the scalar field article defines one as being describable with one number at each point of space. I imagine the actual definition of a scalar field allows multiple numbers to be used, but these numbers should not describe directions? In any case, I'm posting this on the talk to make it noted. Mrfoogles (talk) 03:32, 8 May 2025 (UTC)[reply]

Basically, I think the definition of a scalar field in the lead is inaccurate and needs to be clarified. Mrfoogles (talk) 03:33, 8 May 2025 (UTC)[reply]

I agree with you, and it would be helpful if someone could clarify this (especially at Higgs boson, but here too) so that it not so confusing to people who are trying to understand this rather basic concept. The multi-number idea you describe is simply a fibre bundle that is unrelated to the tangent space, and I do not know whether this elaboration is even needed in the case of the Higgs field. I'm no expert, though. —Quondum 15:50, 8 May 2025 (UTC)[reply]

I just found this source at 28:10 define it by chance -- and a scalar field is at least sometimes defined as one quantity. I think that it might be interesting to mention a fiber bundle/tangent space description, but probably we don't want to put that first as if you don't already know those concepts it's very confusing. I think the deal is that the Higgs field is in fact 4 scalar fields or so -- it's not one scalar field. But people refer to it as scalar anyway because all of its components are.

So, basically, I think the best way to solve this is to just mention in the lead that people sometimes use the term scalar field to refer to fields with multiple scalar components (if a source can be found for that) and mention that the Higgs field specifically is actually 4 scalar fields. Mrfoogles (talk) 20:36, 8 May 2025 (UTC)[reply]

From what I can tell, the primary aspect of it being a "scalar" field in this context is that it is invariant under Lorentz transformations, which is a way of describing it without resorting to less-familiar concepts such as tangent spaces. At Higgs mechanism, it is described as "the standard representation with two complex components called isospin", so it appears to be a quantity that has four real degrees of freedom, but is almost certainly not uniquely separable into four separate real quantities. The video that you link defines a more common definition of scalar, but remember that in physics, words often get repurposed. I've learned to avoid inferring too much from word choice. —Quondum 21:35, 8 May 2025 (UTC)[reply]