Is it advisable to use formal citations in a statement of purpose? In my statement of purpose, I am using certain arguments by scholars of my field (IR). Will it be advisable to use referencing, or might it be to my disadvantage as an unnecessary attempt to boast on my knowledge in that field.
If you're going to use others' ideas or arguments, use citations. 

If you use someone else's ideas in any piece of academic writing, always include citations with sufficient detail for your readers to locate the source of the ideas. To do otherwise would be plagiarism.

Correct attribution of ideas is not boastful; it's a basic requirement of writing.