This chapter begins with a philosophically-oriented outline of quantum field theory that looks at the different ways in which a quantum field can be constructed. The difficulties in articulating a particle ontology are discussed, and it is argued that any putative interpretation of the theory must accommodate the observed particle ‘grin’. A range of metaphysical options are explored, including trope theory and Davudson’s theory of events. The foundations of Fock space are presented in detail from the model-theoretic perspective, and it is suggested that quasi-set theory provides the appropriate formal foundation. Thus, the quanta of quantum field theory can also be accommodated in terms of the overall framework of this work.
Keywords: Fock space, quanta, logic of quanta, quantum field theory, quasi-set theory