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 ...
- 59.3k
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 ...
- 59.3k
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 $\...
- 30.1k
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.) ...
- 39.5k
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