Rename this page to WP:Manual of Style/Physics when complete and universally agreed on by
wikiproject physics.
This part of Wikipedia's
Manual of Style contains guidelines for consistency of style in writing and editing articles on
physics as well as physics-related parts of other articles. For consistency with the rest of Wikipedia, other manuals of style (in particular
WP:MOSMATH for mathematics and
WP:MOSCHEM for chemistry) apply when possible. Exceptions and additional conventions specific to physics topics are described here.
There are a number of different techniques to produce mathematical formulae on Wikipedia, all with their advantages and disadvantages. Inevitably, this has led to a wide spectrum of preferences among editors and of styles used in articles. Even worse, there is a perpetual change of formatting by editors who don't like the current style of an article.
The main principles to be considered when deciding about a particular formatting are consistency and consensus. Don't set one formula in a style very different from the rest of the article, and don't do mass changes from one style to another without prior discussion on the talk page. That said, the style recommended for physics articles is as a rule of thumb:
use wiki markup or the {{math}} template for inline formulae,
use <math>...</math> for displayed formulae.
This choice is aiming at a smooth integration of simple inline formulae in the surrounding text, while offering the extended possibilities of LaTeX formatting for more involved displayed formulae.
Roman versus italic
One of the most basic, though often ignored typesetting conventions for mathematical formulae concerns the use of upright (
roman) versus
italic typeface: as a general rule,
variables (including indices and physical quantities) should be set italic, while
names (including abbreviations, names of particles, chemical elements and units of measurement) should be set in roman type.
This rule explicitly applies also to
subscripts and superscripts. Paying attention to this seemingly minor detail helps to immediately make clear the meaning of a particular notation, and should not be seen as
nitpicking. The rule has a few notable exceptions, which will be explained below.
Greek letters
The
Greek alphabet is extensively used throughout physics and mathematics. Due to technical limitations, the <math>...</math> environment always typesets lower case Greek letters in italic, and upper case ones in roman type. For consistency within an article, Greek letters produced using HTML or {{math}} should thus follow the same convention. This practice applies to both normal and bold font weight.
Lower case Greek letters that denote names of particles, and that don't appear in the same article within a <math> environment, should be set in roman type, following the
general style for names.
Some Greek letters have a second, variant form, for example vs. , vs. , or vs. . If they are used, the same symbol should be used for the same quantity consistently throughout the article. (There is also a variant for the lowercase l in the Latin alphabet, , which can be useful for the distinction from an upper case I.)
One must carefully distinguish quantities, units, and dimensions, because different typographies apply to them. For example:
Voltage is a quantity and may be denoted as V, an
italic capital letter "
V".
The
volt is a unit and must be denoted as V, a roman capital letter. Brackets [] mean the units of, so [V] = V, and braces {} mean the numerical value of so V = {V}[V].
The dimension of voltage should be written in terms of the base dimensions in
roman sans-serif type:[1] ML2T−3I−1.
When a physical constant serves as a unit in some systems, such as in with
atomic units, it should be denoted as a constant (in italics). In particular, the elementary charge, even when treated as a unit, is denoted e, notwithstanding that it was originally a unit (named the electron, with symbol e) (see Elementary charge § As a unit). These symbols are also never prefixed with SI prefixes. Related units that are denoted in roman type include
Generally, all symbols (abbreviations) of units are universally
roman (upright). For dimensions, an exception occurs when denoting the dimension of an arbitrary quantity is necessary, as in "[quantity]"; see
continuity equation for an example of this case.
Representation of units and numerical quantities (where a numerical value and a unit are specified explicitly) should comply with WP:Manual of Style/Dates and numbers § Scientific notation, engineering notation, and uncertainty unless the present Manual specifies otherwise. See also: {{val}}.
Exponential functions are very common in physics, representing growth and decay from solutions of
differential equations,
complex number representations, and
groupgenerators. As such they can have quite large/complicated variables.
For simple arguments on one line, the e notation is legitimate
in which case fractions should use the forward slash /, not \frac{}{}.
however using the forward slash for division as above is acceptable, although extra brackets are usually needed,
whereas fractions using the horizontal stroke are not:
Vectors and vector spaces
For
Euclidean vectors, there are numerous conventions. The better notations for vectors use:
bold: easy to typeset and print, and stands out, easily compatible with other
diacritics, or
or : easy to hand-write and indicates clearly a quantity with direction, although it becomes messy with other
diacritics. Underlining is easily possible in HTML using the <u> </u> tags, like this: A, x. There is the template {{vec}} for HTML left/right/doubleheaded arrows over/under one letter, like this: a→, Z↔ etc.
: is often used for position vectors for example the position vector from point A to B would be written :
In practice, bold italic is also employed, but is less common than upright. For consistency throughout articles, please use upright bold. In particular, please do not execute mass changes from bold style to bold-italic.
A, , not A, ,
For "normal" or
unit vectors, they can be bold, or a hat replaces the arrows:
ê, , not
Quantum state vectors, which are elements of a
Hilbert space, should use the
bra-ket notation, the standard in
quantum mechanics, rather than bold, arrows, or hats. For the bra-ket notation, the {{langle}} and {{rangle}} templates may be used to generate HTML/Unicode equivalents for the \langle and \rangle glyphs of <math> mode. There are also specialized templates {{bra}}{{ket}} for creating bra and ket vectors, and {{bra-ket}} for inner products.
|ψ⟩, ⟨ψ|, |ψ⟩, ⟨ψ|, , not
Operators usually have a hat, but not always (Â vs. A). Either is acceptable as long as the meaning is unambiguous. For example, when describing an
eigenvalue of an operator using the same letter as for the operator itself, the operator should have a hat to distinguish the two.
For tensors not in index notation, use one of sans serif, bold sans serif, bold italic T ... (to be decided). Do not use
𝕓𝕝𝕒𝕔𝕜𝕓𝕠𝕒𝕣𝕕 𝕓𝕠𝕝𝕕, which are reserved for sets (see below
sets and spaces).
The use of
dot product and
del operators for Minkowski space may lead to confusion, especially so in indefinite-metric spaces even between (1, 0)- and (0, 1)-tensors. Also, if the article has to operate with both vectors and higher
tensors, then the use of different styles for tensor fields of different types would be confusing too, even in
3-dimensional space:
vμ∂μf or vμ∇μf, not (∇f )· v.
Subscripts and superscripts
Subscripts and superscripts follow the general rule about
roman versus italic typeface. For example:
Fext, , ,
rather than
Fext, , .
Note that in the last example, "ext" is a text label (an abbreviation for "external") and is thus set roman, while x0 is a variable and is this set in italic. This type of notation is sometimes used instead of Bext(x0, t) to indicate that only the functional dependence of B on t is of interest, while x0 is a parameter held fixed (though conceptually still a variable).
An exception can be made when the
<math> tag has to be used, and an intended glyph is not available in
its renderers, such as non-italicized Greek letters. For example, when typesetting the mass of a
neutrino ν (nu) in html or {{math}}, the ν can remain non-italic:
Generally, the first is used in simpler contexts, while index notation is used to make advanced manipulations simpler. The
linear operator notation is depreciated (with possible exception of
theoretical mechanics and other domains where index notation is traditionally avoided).clarification needed
Letters that areindices for
tensors or
spinors (see for example
Ricci calculus and
Van der Waerden notation) should be italicized. A specific script used as a tensor index may give a hint about nature of the corresponding linear space – this distinction should be used whenever possible. For example,
spacetime-based (four dimensional) objects should be indexed with a subset of lowercase
Greek letters:
Aμ or
Ideally - not all Greek letters are used for indices. For example, ϕ and ψ are excluded due to its heavy usage as wave functions and fields, and η is used to denote the
standard (Minkowskian) metric.
(although the letters i, j may cause confusion where
complex numbers are used; this should be clarified in the context),
Ak or
Note that {{ell}} is equivalent to
ℓ. Distinction of indices is especially helpful when one tensor quantity is built on
several linear spaces of different natures.
Calculus
If "d" is used in
differentials or
derivatives, it should be italic or upright throughout; mixed styles look irregular.
In vector expressions for the gradient ∇, with respect to a given basis, the basis vectors should be in front of the derivative operators. In
3dCartesian coordinates:
∇ = êx∂/∂x + êy∂/∂y + êz∂/∂z or
and not
∇ = ∂/∂xêx+ ∂/∂yêy + ∂/∂zêz or
and similarly for any other coordinates. It is clear this way that the derivatives are operators not acting on the basis vectors (which can have spatial dependence in a local coordinate frame).
When using <math>, use either (\nabla) or (\bigtriangledown ) throughout - it looks irregular to mix the styles.
The capital delta symbol is universally reserved for changes in quantities, for example Δx for change in position coordinate x.
The same symbol Δ is also used in mathematics to denote the
Laplacian operator. Where possible, please use the "nabla squared" symbol ∇2, which appears to be more common in physics, and is more intuitive; ∇2 = ∇ ⋅ ∇ is a nicer notation, and less ambiguous for capital delta.
The symbol ∂α is used for the
four gradient operator (indexed components), as usual. There are other notations, including
For integrals, either of the notations are employed in the literature:
∫ f(x) dx, ∫ dxf(x) or
and either is acceptable in WP physics articles.
For {{math}},
integral symbols can be produced using the same syntax as for LaTeX using the {{intmath}} template.
For integrations over the
boundary of a (hyper)volume V, the partial symbol ∂ denoting the boundary of a closed volume is encouraged (including a brief explanation such as "where ∂V is the boundary of the volume V"); it is a powerful and compact notation:
∫ ∂V ψ(x) dV or
and removes the need to use another symbol for the boundary of the volume.
There is an
abuse of notation where integrands are not enclosed in brackets, frequently the case when (say)
Green's theorem in a 2d plane is applied:
∮ ∂Dp(x, y) dx + q(x, y) dy or ,
which really means:
∮ ∂D [ p(x, y) dx + q(x, y) dy ] or
The brackets are often dropped by sources since it is known the integral symbol always includes the differentials (in the above example "dx" and "dy"). Nevertheless: for the sake of clarity an extra pair of brackets will not clutter, and should be included.
Ratios of differential (infinitesimal) quantities and derivatives
In physics, ratios of
differential (infinitesimal) quantities frequently occur, and share the same notation with first order
derivatives, which also frequently occur. For example, the local
charge density of an electrically charged continuum is given by the ratio of the infinitesimal charge dq in infinitesimal volume dV:
However, this looks like a derivative of q with respect to V. In cases like this, notations can be misleading, as
Used only for derivatives, not ratios as above. Advantages include:
makes clear that differentiation is an operator,
clarifies notation for higher derivatives by repeated action of a derivative,
dn/dxny = d/dx...d/dxd/dxy
For partial derivatives this is not a problem, since differentials are never written as "∂x"; only the full symbol of a partial derivative, in any of the equivalent notations;
∂F/∂x, ∂/∂xF, ∂F⁄∂x, ∂⁄∂xF, ∂F/∂x,
has meaning.
Particles, substances and reactions
Symbols for subatomic particles and nuclei can be generated with {{Subatomic particle}} and
Nuclide templates, otherwise they should be typographically similar.
Where chemical notation is used, it should comply with
WP:MOSCHEM.
Formulae of (nuclear or particle) reactions should not be formatted with <math> or {{math}}. Use templates, wiki code formatting, and HTML tags to match the main text, both for inline and displayed formulae.
For all reactions, the arrow symbol → should be used, the equals sign = is usually wrong.
An article can usually not give a detailed explanation of all concepts and nomenclatures used to explain its topic. Some basic knowledge of physics and mathematics will generally be required of the reader, to an extent depending on the article's subject. However, where appropriate, links to more introductory articles and
summary style descriptions of the essential concepts should be provided.
Physics
A large number of
physical theories exist, and compatibility between them varies. Concepts as
distance,
time and
mass appear to be universal, although their exact definitions can depend on the subject. Unless an article deals explicitly with these fundamental concepts, it should not explain the meaning of distance, time or mass.
Expected units
The following everyday units are presumed to be known and needn't be explained, although ideally linked at least once.
Old non-SI units (such as "
erg", "
dyne", "
knots" etc.), and
imperial units, ideally should only to be used for:
historical relevance,
within context relevant to those main articles,
if references (databooks, handbooks, appendices of books etc.) present measurements in terms of those units.
In general, SI units are usually assumed by most people. When using other unit systems which are extensively employed in practice although may be unfamiliar to laymen, including:
it should be explicitly stated they are going to be used before using them. There are several sets of natural units, each with their own applications, so which one must be clear. Ideally, natural units shouldn't be used, due to lack of familiarity and potential confusion by many readers. For example: giving masses of
elementary particles in MeV when the reader thinks of kg (or decimal prefixes thereof) is confusing, a related point is that writing "E = m", without referring to natural units, is confusing when the reader expects the c2 factor...
As a rule of thumb (for natural units):
They could be used in some calculations or explanations to illustrate how and why natural units are better than SI units in the process,
if the calculation/explanation can easily be done in SI units, use SI units, and not natural units for the sake of it.
Clarifying the relevant physics
Physics is such an enormous subject that an article should specify the relevant branch(es) of it, unless the concept is physically universal. Known academic paradigms, with usual abbreviations, are:
Quantum field theory (QFT, implies QM, SR, background in classical field theory) – not necessary to mention if one of well-known derived theories is used directly:
Any abstract notation which requires additional irrelevant explanation (i.e.
set builder notation,
symbolic logic notations, especially
quantifier notation, others?), are not to replace worded descriptions for the sake of compact mathematical statements - they simply create more work in explaining and linking the notations, while contributing no understanding to the physics at hand.
To exemplify:
Even if the context becomes abstract, statements like
"x is a number such that x ∈ ℝ: x > 0, where ∈ denotes "
element of a
set", the colon means "such that", and ℝ denotes the
real numbers"
are too long, cluttered, and confusing for non-expert mathematicians: simply write
"x is a
real number greater than and not equal to zero"
since this way explains the context without introducing unfamiliar notations.
which makes it very clear to anyone that j takes those values and the sequence of numbers is infinite. Even though the full
set builder notation:
j ∈ {0, 1⁄2, 1, 3⁄2...}, or j ∈ {n/2 : n ∈ ℕ0}, etc.
is technically more correct, this is actually less clearer to a typical reader, since the symbols have to be explained by editors and/or read up by readers.
"The zeroth law can be stated as (TA = TC) ∧ (TB = TC) ⇒ (TA = TB) where ∧ means "and", ⇒ denotes "imples", and TA, TB, TC are the temperatures of objects A, B, C."
may be compact, but is pointless since the notation has to be explained (constituting no thermodynamics). The law can be stated in words:
"Letting TA, TB, TC denote the temperatures of objects A, B, C, if A is in thermal equilibruim with C (so TA = TC), and B is in thermal equilibruim with C (so TB = TC), then A and B are in thermal equilibruim with each other (TA = TB)."
Levels of difficulty
The tables below (mainly of numbers,
operations, and functions required to build formulae) are roughly grouped into three levels of difficulty; school/(advanced) college level, then undergraduate level, finally graduate level (and beyond). Articles which fall into one (or between?) these sections should consider the reader to assume some familiarity within the scope of the section.
In all cases, the numbers, operations etc.:
should be linked to the main articles
not require any in-depth explanation (a few words or sentence at most).
Of course, other operations not tabulated can be used, provided their use is declared and linked. Most of the operations not tabulated below will be outside the scope of most of physics, such as some non-elementary functions like
tetration, super-roots, and
super-logarithms, and hence no prior knowledge of the reader is required.
etc., then
i (or j) is presumed to be known too, although the context should state it is the imaginary unit and not something else, like a summation dummy variable or tensor indices.
Templates can be used for linking groups of articles, in the form of:
sidebars: boxes of links with collapsible sections, usually placed in the top right corner of an article, and
navboxes: boxes of links which are fully collapsible, usually placed at the very end of the article, even after the
"see also",
"references", and
"external links" sections.
A decision at each article should be made for what kind of template of links to use. Sidebars are a matter of debate for their size and layout of links; some favour their use, others oppose or are neutral. Navboxes are usually less problematic due to their compactness.
Often, an article is well-served with a picture, diagram, or even an animation (see
wavefunction for a good example), at the very top to provide an immediate visual depiction of what the article says.
An image directly corresponding to the specific topic of an article should have priority for putting in the top right corner over a sidebar template.
Placing an image in the center, while placing a template in the corner, creates large amounts of whitespace, and the
table of contents only adds more whitespace. Both can be avoided by having the image floating in the top-right corner and the sidebar below, or replacing the sidebar with a navbox.
Some pages on abstract topics, where it's hard to find an image that's clearly associated with the article, (e.g. articles related to
string theory), may benefit from an "icon" inside a sidebar. This can immediately inform the reader about the substance of the article, while including the links to related articles at the same, hence sidebars may be useful in cases like this.
Templates with a lot of links (say, 50 or more) are better as footers than as sidebars, since opening the sections of a sidebar makes it extend a long way down the page, and makes the box and article less readable this way.
It is legitimate to place navboxes in the "see also" or "references" sections if that's where the article ends. Placing navboxes in "see also" sections is beneficial as they display a large collection of related links in one place with minimum wikicode (only template syntax is needed).
If the contents of a template only has partial relevance to the article; they are likely to contribute to
template creep, and hence should not be used.
If neither are suitable for any reason, the best resort is to just use the
categories of the article.
Conventions in WP articles and sources
Aside from units, there are cases where specific choices of mathematical entities have to be made, notably the
metric tensors in SR and GR, and the representations of the
gamma matrices.
Sometimes, reliable and well-established sources use conventions which may lack a clear physical depiction, and WP editors should consider what the best conventions a physics article should have.
Maxwell's equations in
differential forms are an example (the 4-current is preferred as a 3-form, but sources (including
Gravitation) use the 4-current as a 1-form, see the article
Mathematical descriptions of the electromagnetic field for this).
Editors should:
decide what conventions are the easiest for a reader to follow and for internal consistency, and also state clearly (in a section or footnotes?) the prominent alternative conventions used by other authors,
^In pure mathematics, for a complex vector v its conjugate v is an element of the
complex conjugate vector space. Although the complex conjugate of a vector is used in physics (for example, in ⟨ψ|A|ψ⟩), the notation with overline is discouraged except for aforementioned two cases.
Further reading
AIP style manual(PDF). prepared under the direction of the AIP Publication Board (4th ed.). New York, N.Y.: American Institute of Physics. 1990.
ISBN0-88318-642-X.{{
cite book}}: CS1 maint: others (
link)