On Bargmann Representations of Wigner Function
arXiv:0712.2704 · doi:10.1088/1751-8113/41/5/055305
Abstract
By using the localized character of canonical coherent states, we give a straightforward derivation of the Bargmann integral representation of Wigner function (W). A non-integral representation is presented in terms of a quadratic form V*FV, where F is a self-adjoint matrix whose entries are tabulated functions and V is a vector depending in a simple recursive way on the derivatives of the Bargmann function. Such a representation may be of use in numerical computations. We discuss a relation involving the geometry of Wigner function and the spacial uncertainty of the coherent state basis we use to represent it.
accepted for publication in J. Phys. A: Math. and Theor
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