Some journals require upright Greek letters for constants as opposed to variables, for example $\upi$ when used to denote 3.14159... as opposed
to a variable ($\pi$ is sometimes used to denote parallax in astronomy,
for instance). (Some journals define \upi as "upright pi", \upi as
"upright i", and so on.)

I certainly agree that LABELS should be upright (though they are usually
Latin not Greek) and not italic to distinguish them from variables, e.g. $T_{mathrm{eff}}$ for effective temperature or $\rho_{textrm{g}}$ for
gas density, say, as opposed to $G_{\mu\nu}$ where $\mu$ and $\nu$ are
not constants but variables.

And it is not just Greek letters. For example, e for the Euler number
or i for the square root of -1 should also not be in math italic, to distinguish them from variables. I tend to agree with that as well.
Also, units should be upright, e.g. 5 m and not $5m$ for 5 metres.

On the other hand, I have never seen the gravitational constant $G$,
which is even by definition a constant and not a variable, written
upright. Ditto for the Hubble constant $H$ and so on.

Or is there a difference between mathematical constants and physical
constants?

Perhaps because standard (La)TeX provides Greek letters only in math
italic, upright Greek letters are less common than upright Latin
letters, even when used in the same way (labels, units, symbols which
are not variables).

When writing for a specific journal, one usually has to follow the house
style. However, if there is no rule, I prefer to do what is generally
deemed to be correct. What is generally deemed to be correct here?

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On 2020-04-27 00:05, Phillip Helbig (undress to reply) wrote:

Some journals require upright Greek letters for constants as opposed to variables, for example $\upi$ when used to denote 3.14159... as opposed
to a variable ($\pi$ is sometimes used to denote parallax in astronomy,
for instance). (Some journals define \upi as "upright pi", \upi as
"upright i", and so on.)

...

Or is there a difference between mathematical constants and physical constants?

The principle probably comes from pure mathematics, but even there, historically, they have not been available, just as well certain styles,
such as bold italic, for the simple reason that it was expensive in led typesetting to keep them. Some journals would though have them, and one
could mark up the manuscript to get the right one.

Unicode changed that by adding those as characters (code points), in
addition adding some styles that are not properly semantic, like sans
serif and monospace variations. (The sans serif style is used for
tensors by some engineers, but I have found no example in mathematics,
physics or computer science of that.)

[[Mod. note -- Checking a few general-relativity textbooks, I see that
Misner, Thorne, & Wheeler "Gravitation" (W.H. Freeman, 1973) uses sans
serif for tensors and differential forms, but none of the other books
I checked do this.
-- jt]]

So when those are available, one can experiment with adhering to this principle, upright for constants and italic/slanted for variables.

In some cases it may not be immediately clear what to use: Unicode
unifies the upright style with the original language letters.

TeX, by contrast, translates them automatically to italic in math mode.
For Greek, it only has the slanted styles, and in addition not the
uppercase letters that look like the Latin.

Perhaps because standard (La)TeX provides Greek letters only in math
italic, upright Greek letters are less common than upright Latin
letters, even when used in the same way (labels, units, symbols which
are not variables).

So I switched typing these mathematical styles directly in the input
file, and the fastest way to do that, both to implement and use, I found
is to use text substitutions. Then the LaTeX unicode math package was insufficient, so I switched to ConTeXt.

When writing for a specific journal, one usually has to follow the house style. However, if there is no rule, I prefer to do what is generally
deemed to be correct. What is generally deemed to be correct here?

You will have to experiment with it a bit.

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On 2020-05-16 05:09, Mod wrote:

Unicode changed that by adding those as characters (code points), in
addition adding some styles that are not properly semantic, like sans
serif and monospace variations. (The sans serif style is used for
tensors by some engineers, but I have found no example in mathematics, physics or computer science of that.)

[[Mod. note -- Checking a few general-relativity textbooks, I see that Misner, Thorne, & Wheeler "Gravitation" (W.H. Freeman, 1973) uses sans
serif for tensors and differential forms, but none of the other books
I checked do this.
-- jt]]

They use bold sans-serif when not having indices, but switches to
non-bold serif, that is, plain italic, when having indices on the same
object. In mathematics, like in differential geometry, one uses serifs
and not switching styles, like between plain and bold, allowing the
styles to be used for more different types of objects objects.

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