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,

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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,

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Or is it really that SI units specifically should be in roman font, and everything else should be italicized?

  • I guess SI also specifies which are the valid unit symbols. Otherwise, I can just claim that I'm using an unit symbol called "mile" which is equal to 1609.344 m, and I'm perfectly compliant with SI. – Federico Poloni Nov 29 '18 at 17:15
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    Note, however, that in the first equation the subscript "p" should be upright because it's not a quantity or a numerical value but stands for proton. – Massimo Ortolano Nov 29 '18 at 20:09

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.

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