ABSTRACT. In this talk we want to present the recent results of \cite{DK}. We construct several smooth classical denotational models of Linear Logic: they are smooth as non-linear proofs are interpreted as infinitely differentiable functions, and they feature an involutive linear negation. The starting point of this work consists in noticing that the multiplicative disjunction $\parr$ corresponds to the well-known Schwartz' epsilon product. Requiring its associativity then asks for a completeness notion, while the linear involutive negation is ensured by considering a good topology (the Arens topology) on the dual, ensuring that the linear involutive negation works as an orthogonality relation.