DIRECT QUANTIZATION OF EQUATIONS OF MOTION: FROM CLASSICAL DYNAMICS TO TRANSITION AMPLITUDES VIA STRINGS

作者：Kochan Denis^*

来源：International Journal of Geometric Methods in Modern Physics, 2010, 7(8): 1385-1405.

DOI：10.1142/S0219887810004865

• Quantization of dissipative systems
• umbilical strings
• path vs. surface integral

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.

• 出版日期2010-12