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- TL;DR Summary
- I am wondering how a quantum field can be represented as a tensor product of a vector space and an endomorphism of a subspace of a Hilbert space (which is how it is represented in a paper I am reading about the Whitman Axioms), and what this tensor product actually represents.

Sorry in advance if this question doesn't make sense.

Anyway, I am reading a paper about quantum field theory and the Whitman Axioms (http://users.ox.ac.uk/~mert2060/GeomQuant/Wightman-Axioms.pdf), and it describes a field (Ψ) as

Ψ:𝑀→𝑉⊗End(𝐷)

where 𝑀 is a spacetime manifold, 𝑉 is a vector space, and 𝐷 is a dense subspace of a Hilbert space. My question is what 𝑉⊗End(𝐷) physically represents?

Once again thanks for any help.

Anyway, I am reading a paper about quantum field theory and the Whitman Axioms (http://users.ox.ac.uk/~mert2060/GeomQuant/Wightman-Axioms.pdf), and it describes a field (Ψ) as

Ψ:𝑀→𝑉⊗End(𝐷)

where 𝑀 is a spacetime manifold, 𝑉 is a vector space, and 𝐷 is a dense subspace of a Hilbert space. My question is what 𝑉⊗End(𝐷) physically represents?

Once again thanks for any help.