2
$\begingroup$

In elementary quantum mechanics, we learn that quantum observables are self-adjoint operators that act on the Hilbert space of states.

However, in more advanced context, we talk of local operators, which are supposed to be quantum observables supported locally, forms an algebra.

First, there is the Weyl algebra appearing in deformation quantization. It is the universal enveloping algebra of the Heisenberg Lie algebra, and obtained by deforming the the space of classical observables.

Second, in CFT, we assume operator product expansion. By multiplying two fields, we obtain another.

I would be grateful to anybody who could clear things out for me.

Improve this question
$\endgroup$
1
  • 2
    $\begingroup$ There is a one-to-one correspondence between self-adjoint operators and their spectral measures, so one can describe quantum observables by spectral measures on a Hilbert space, which then form an algebra (Jordan algebra). $\endgroup$ Commented Feb 20, 2022 at 13:06

0

Reset to default

You must log in to answer this question.

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.