Functional integral for non-Lagrangian systems

Jan, 2010
14 pages
Published in:
  • Phys.Rev.A 81 (2010) 022112
e-Print:

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Abstract: (arXiv)
A novel functional integral formulation of quantum mechanics for non-Lagrangian systems is presented. The new approach, which we call "stringy quantization," is based solely on classical equations of motion and is free of any ambiguity arising from Lagrangian and/or Hamiltonian formulation of the theory. The functionality of the proposed method is demonstrated on several examples. Special attention is paid to the stringy quantization of systems with a general A-power friction force κ[q˙]A-\kappa[\dot{q}]^A. Results for A=1A = 1 are compared with those obtained in the approaches by Caldirola-Kanai, Bateman and Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon approach are discussed as well.
Note:
  • 14 pages, 7 figures, corrected typos
  • 11.10.Ef
  • 03.65.Ca
  • 31.15.xk
  • field equations: classical
  • Hamiltonian formalism
  • quantum mechanics
  • Lagrangian formalism
  • path integral
  • quantization
  • string