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- Physicist-friendly explanation of "symbol ##\phi(f)##", please?

I'm probably inadequately equipped to understand this paper by Bucholtz, Longo and Rehren on "

*Causal Lie products of free fields and the emergence of quantum field theory*", but I decided to give it a try. Alas, I got stuck in the 1st para of sect 2 where it says:Although I've seen the term "We consider a Lie algebra ##\Phi## that is generated by the symbols ##\phi(f)## which are real linear with regard to ##f \in \mathcal{s}(\mathbb{R}^d)##. [...]

*symbol*##\phi(f)##" before, I've never succeeded in properly understanding what it means. Could someone please explain the meaning of this use of "symbol" in a physicist-friendly way?