Quoting from the link (emphasis mine): > symmetrized __tensor product__ of n single-particle Hilbert spaces H And clarifying your statement by copying from t

Quoting from the link (emphasis mine): > symmetrized __tensor product__ of n single-particle Hilbert spaces H And clarifying your statement by copying from the wiki page (emphasis mine): > direct sum of the symmetric or antisymmetric tensors in the __tensor powers__ of a single-particle Hilbert space (which is very different from the direct sum you suggest in your comment) I work with all of this in my day job and the research work I produce (which does deal a lot with quantum description of multiples modes of light) is usually perceived as correct by my academic colleagues. I am honestly trying to see how to interpret what you are saying differently, in a way that does not clash with the established knowledge on the topic, but I can not, even though I have non-negligible experience in the field. At best, I assume we are talking past each other while describing the same thing, but I am certainly uncomfortable with your use of "subspace" and "direct sum". Going to the very first comment of yours that started this: My claim is that a mode (something that has a creation operator) can very well contain one, or two photons, or a coherent state, or anything else from its Hilbert space. There is no correspondence between plane waves and Fock states. We can use Fock states with other modes instead of plane waves, and we can have plane waves with a quantum state that is a coherent state for instance.