On the Rigged Fock Space

Rigged Hilbert Spaces (RHS), also called Gelfand Triplets, are being used increasingly in Mathematical Physics. One of its versions, the Rigged Fock Space (RFS), has had little place in the literature, even in the literature on Quantum Field Theory. This is a review paper on RFS in which we reformulate some well-known notions in the proper language of RHS, which also implies the use of the terminology and techniques of locally convex linear spaces. We introduce appropriate locally convex topologies to construct our RFS. Within this context, we revise the construction of creation and annihilation operators, or the Gamow states for an unstable interaction between fields, as continuous linear mappings with those topologies. We revise the construction of an algebra of continuous operators from the test space to its dual on RFS.