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The SI conventions state that variables and quantity symbols should be italicized, while unit symbols should be roman (see, e.g., this useful reference/cheat sheet). For example,
Here the proton mass (m_p) is being used as a quantity. But you could use the same quantity as a unit, in which case should you use a roman font? For example,
Or is it really that SI units specifically should be in roman font, and everything else should be italicized?
The general approach (see e.g. NIST or IUPAC for sources) is to consider physical constants, such as the proton mass, as quantities. They are thus usually italicized, even when used as units.
Certain units, notably the electronvolt (eV) and the atomic mass unit (u), are considered so important that they are "accepted for use with the SI system", see the SI brochure. These should be given in roman type.
