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Not sure if this is a silly question, but: is there a standardised symbol or abbreviation that can be used in formal definitions to refer to particles?

Writing "PARTICLE" or "PART" sounds...silly...

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In interlinear glosses, I think PTC or PTCL are most commonly used to abbreviate "particle".
PRT or PART are sometimes used too, but should rather be avoided due to confusion with "preterite" and "participle", respectively.
But the name actually doesn't matter that much given that you provide a list of the abbreviations that you used with their intended meaning (which is always good practice to do because of the lack of a definite universal standardisation).

In formal definitions, I generally wouldn't use abbreviations but always terminology as precise as possible.

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