Denis Kochan
Quantization of dissipative systems
Geometrical formulation of classical mechanics with forces that are not necessarily potentialgenerated will be presented. Time evolution in that case is governed by certain canonical twoform $\Omega$, which is constructed purely from forces and the metric tensor entering the kinetic energy of the system.
New type of variational principle employing differential twoform $\Omega$ and
umbilical strings will be introduced. The Feynman path integral over histories of the system will be then rearranged to umbilical worldsheet functional integral in accordance with the proposed variational principle. In the case of potentialgenerated forces, worldsheet approach reduces to the standard quantum mechanics. As an example
Quantum Mechanics with friction will be analyzed in detail.
