collected some references on the interpretation of the !-modality as the Fock space construction at *!-modality*.

Cross-linked briefly with he stub entries_Fock space_ and *second quantization*.

David C. has kindly created a list of references at *Geometry of Interaction*. I have now started there an Idea section:

]]>What has been called

Geometry of Interaction(Girard 89) is a kind of semantics for linear logic/linear type theory that is however different in method from the usual categorical semantics in monoidal categories. Instead of interpreting a proof of linear implication $A\multimap B$ as a morphism between objects $A$ and $B$ in a monoidal category as in categorical semantics, theGeometry of Interactioninterprets it as an endomorphism on the object $A\multimap B$. This has been namedoperational semanticsto contrast with the traditionaldenotational semantics.That also the “operational semantics” of GoI has an interpretation in category theory, though, namely in traced monoidal categories was first suggested in (Joyal-Street-Verity 96) and then developed out in (Haghverdi 00, Abramsky-Haghverdi-Scott 02,Haghverdi-Scott 05).

The following simple thought must have been voiced and discussed before, where?

Namely there is some relation between categorical semantics for (the multiplictive fragment of) linear type theory in which each monomorphism is a split monomorphism and the notorious concept known as “collapse of the wave function” in quantum physics:

Since monomorphisms are the semantics of propositions, if they all split then equivalently projections become semantics for propositions. We may then think of inspecting the truth of a proposition by applying the corresponding projection. But that projection is just the “wave function collapse”.

This thought must have been expressed before. Where?

]]>just for completeness so that I don’t have gray links elsewhere, I have created some minimum (nothing exciting) at *quantum fluctuation*.

felt like making a terminological note on *phase and phase space in physics* (and linked to it from the relevant entries).

If anyone has more information on the historical origin of the term “phase space”, please let me know.

]]>added to C-star algebra a stub section on the dagger-categorical formulation

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