抄録
The Wigner representation Fs(p, q) of a quantum operator F(p, q) is defined by Fs(p, q)=h\Tr F(p, q)Δ(p−p, q−q) where Δ is a quantum analogue of a delta function in the phase space. This gives in particular the Wigner distribution function for a density operator. Basic theorems are summarized for the computation rules for quantummechanical operators in the Wigner representation. This is applied, in particular, to electrons in a magnetic field, for which a Wigner d. f. is introduced to describe the distribution of physical momenta \vecπ=m\vecv, \vecv being the velocity, and the position x. This description has the advantage to avoid the use of a vector potential and so to be gauge-independent. As examples of application, the diamagnetism and the Hall effect are briefly treated. Further applications of this treatment will be published later.
