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In the first part of the paper I investigate categorical models of multiplicative biadditive intuitionistic linear logic, and note that in them some surprising coherence laws arise. The thesis for the second part of the paper is that these models provide the right framework for investigating differential structure in the context of linear logic. Consequently, within this setting, I introduce a notion of creation operator (as considered by physicists for bosonic Fock space in the context of quantum field theory), provide an equivalent description of creation operators in terms of creation maps, and show that they induce a differential operator satisfying all the basic laws of differentiation (the product and chain rules, the commutation relations, etc.).