The relevance of a document has many facets, going beyond the usual topical one, which have to be considered to satisfy a user's information need. Multiple representations of doc- uments, like user-given reviews or the actual document con- tent, can give evidence towards certain facets of relevance. In this respect polyrepresentation of documents, where such evidence is combined, is a crucial concept to estimate the relevance of a document. In this paper, we discuss how a ge- ometrical retrieval framework inspired by quantum mechanics can be extended to support polyrepresentation. We show by example how different representations of a document can be modelled in a Hilbert space, similar to physical systems known from quantum mechanics. We further illustrate how these representations are combined by means of the tensor product to support polyrepresentation, and discuss the case that representations of documents are not independent from a user point of view. Besides giving a principled framework for polyrepresentation, the potential of this approach is to capture and formalise the complex interdependent relationships that the different representations can have between each other.
