Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-03-08
Int.J.Geom.Meth.Mod.Phys.07:1385-1405,2010
Physics
High Energy Physics
High Energy Physics - Theory
16 pages, 5 figures, comments are welcome, author is looking for postdoctoral position
Scientific paper
10.1142/S0219887810004865
New method of quantization is presented. It is based on classical Newton-Lagrange equations of motion (representing the fundamental physical law of mechanics) rather than on their traditional Lagrangian and/or Hamiltonian precursors. It is shown that classical dynamics is governed by canonical two-form $\Omega$, which embodies kinetic energy and forces acting within the system. New type of variational principle employing differential two-form $\Omega$ and ''umbilical strings'' is introduced. The Feynman path integral over histories of the system is then rearranged to ''umbilical world-sheet'' functional integral in accordance with the proposed variational principle. In the case of potential-generated forces, world-sheet approach reduces to the standard quantum mechanics. As an example Quantum Mechanics with friction is analyzed in detail.
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