Quantization of dissipative systems - some irresponsible speculations

The Newton-Lagrange equations of motion represent the fundamental law of mechanics. Their traditional Lagrangian and/or Hamiltonian precursors when available are essential in the context of quantization. However, there are situations that lack Lagrangian and/or Hamiltonian settings. This paper discusses classical and quantal dynamics of such systems and presents some irresponsible speculations by introducing a certain canonical two-form Ω. By its construction Ω embodies kinetic energy and forces acting within the system (not their potential). A new type of variational principle is introduced, where variation is performed over a set of 'umbilical surfaces' instead of system histories. It provides correct Newton-Lagrange equations of motion and something more. The quantization is inspired by the Feynman functional integral approach. The quintessence is to rearrange path integral into an ''umbilical world-sheet'' integral in accordance with the proposed variational principle. In the case of potential-generated forces, the new approach reduces to the standard quantum mechanics