Abstract

It has been observed by several people that, in certain contexts, the free symmetric algebra construction can provide a model of the linear modality ! . This construction arose independently in quantum physics, where it is considered as a canonical model of quantum field theory. In this context, the construction is known as (bosonic) Fock space. Fock space is used to analyze such quantum phenomena as the annihilation and creation of particles. There is a strong intuitive connection to the principle of renewable resource, which is the philosophical interpretation of the linear modalities. In this paper, we examine Fock space in several categories of vector spaces. We first consider vector spaces, where the Fock construction induces a model of the\Omega ; &; ! fragment in the category of symmetric algebras. When considering Banach spaces, the Fock construction provides a model of a weakening cotriple in the sense of Jacobs. While the models so obtained model a smaller fragment, it is cl...