4 votes

Condition for an operator on a quantum Hilbert space to behave like vector

It depends on the precise rigorous definition of a vector of selfadjoint operators. Usually, there is a dense invariant subspace for the operators and the generators of rotations, where all linear ...
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3 votes

How do *-Algebras correspond to operators on a Hilbert space?

Why are 𝐶∗-Algebras enough for flat spacetime/not enough for curved spacetime? They are not enough even for flat spacetime. They are enough in both cases as far as you restrict your interest to the ...
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1 vote

Rigorously building a Fock space, creation/annihilation operators and inner products in a QFT

The Fock space is a mathematical construction that starts from one initial Hilbert space, called the one-particle Hilbert space in Physics, and builds a new Hilbert space out of it. Basically, let $\...
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1 vote

Condition for an operator on a quantum Hilbert space to behave like vector

If you multiply $A_k$ by the same scalar function $f(r)$, then $f(r)\vec A$ remains a vector so since $f(r)$ is otherwise pretty arbitrary there are (up to some technical stuff like domains etc.) ...
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