# Physical Meaning of a Quantum Field

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

$$Ψ:M\rightarrow V\otimes\text{End}(D)$$

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 $$V\otimes\text{End}(D)$$ physically represents?

Once again thanks for any help.

• As written, the question is unanswerable. What it "represents" depends on what exactly $D$ and $V$ are and what theory exactly you are talking about (i.e. what Lagrangian). The meaning is very different if it is a gauge field vs. a spinor field vs. a Goldstone boson vs. ... – ACuriousMind Sep 6 '19 at 22:00
• The Hilbert space? – G. Smith Sep 6 '19 at 22:18
• Perhaps you could cite the relevant paper for context. – J. Murray Sep 6 '19 at 22:53
• The paper is about the Whitman Axioms: users.ox.ac.uk/~mert2060/GeomQuant/Wightman-Axioms.pdf – Bobjoesmith Sep 8 '19 at 23:54