All Questions
3
questions
1
vote
1
answer
122
views
Obtaining the star product from the Weyl quantisation of the product of two symbols
It can be shown (Groenewold 1946) that the Weyl quantisation of the product of two Weyl symbols is given by
$$ [A(\textbf{r})B(\textbf{r})]_{w}=\frac{1}{(2\pi)^{2}}\int_{\mathbb{R}^{4}}e^{i\...
4
votes
1
answer
441
views
Non-commutative Fourier transform of an operator
Wigner-Weyl transform relates an operator to its distribution function in phase space through an operator Fourier transform which is said to be non-commutative.
$$
\hat{\rho} \xrightarrow[non-comm]{...
1
vote
4
answers
1k
views
Definition of symmetrically ordered operator for multi-mode case?
As I know, Wigner function is useful for evaluating the expectation value of an operator. But first you have to write it in a symmetrically ordered form. For example:
$$a^\dagger a = \frac{a^\dagger ...