The Phase Space Formulation of Time-Symmetric Quantum Mechanics, I: the Wigner Formalism

Time-symmetric quantum mechanics can be described in the usual Weyl–Wigner–Moyal formalism (WWM) by using the properties of the Wigner distribution, and its generalization, the cross-Wigner distribution. The use of the latter makes clear a strongly oscillating interference between the pre- and post-selected states. This approach allows us to give explicit formulas for the state reconstruction problem, thus generalizing known results to the case of arbitrary observables. In a forthcoming paper we will extend these results to other quantization schemes.