Functional integral for non-Lagrangian systems

Abstract

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 $-\kappa [\dot{q}{]}^A$. Results for $A=1$ 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.

14 pages, 7 figures, corrected typos

References in corpus (3)

• Quantizing non-Lagrangian gauge theories: an augmentation method
• Canonical quantization of so-called non-Lagrangian systems
• How to Quantize Forces(?): An Academic Essay How the Strings Could Enter Classical Mechanics

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