Finite dimensional complex linear spaces with indefinite metrices will be constructed by using Weyl's method. The triangular inequality does not hold valid in these spaces....
An attempt is made to construct quantum mechanics in one dimension on the basis of finite displacements. Replacing the differential operator by a difference operator indicates a possibility of using a right or left difference and further, that the state vector is a 2-spinor. An indefinite metric is introduced in this spinor space with respect to which the displacement operators in two opposite directions are hermitian conjugates. After further operations, the formalism obtained can be generalized to the case of a complex plane. Its generalization to the whole space can be effected along Weizacker's ideas of a fundamental alternative. (auth)