Introduction to Quantum Mechanics from a Geometrical Point of View

J. Anandan

Vladimír Majerník

Luigi Barletti

The paper is devoted to review, from a mathematical point of view, some fundamental aspects of the Wigner formulation of quantum mechanics. Starting from the axioms of quantum mechanics and of quantum statistics, we justify the introduction of \nthe Wigner transform and eventually deduce the Wigner equation.

Minic, D, Hsiung Chia Tze

We propose a generalization of the standard geometric formulation of quantum mechanics, based on the classical Nambu dynamics of free Euler tops. This extended quantum mechanics has in lieu of the standard exponential time evolution, a nonlinear temporal evolution given by Jacobi elliptic functions. In the limit where latter's moduli parameters are set to zero, the usual geometric formulation of quantum mechanics, based on the Kahler structure of a complex projective Hilbert space, is recovered. We point out various novel features of this extended quantum mechanics, including its geometric aspects. Our approach sheds a new light on the problem of quantization of Nambu dynamics. Finally, we argue that the structure of this nonlinear quantum mechanics is natural from the point of view of string theory.

J. Anandan

H. O. Girotti

The functional formulation of quantum mechanics and relativistic quantum field theories are widely studied subjects. Nevertheless, certain aspects of this formulation are frequently overlooked, in spite of their relevance from a structural point of view. This book aims to fill up this gap. The non-relativistic regime has been found particularly appropriate for these purposes.