Functional integral for non-Lagrangian systems

TL;DR

This paper introduces a new functional integral method called 'stringy quantization' for quantum systems without a Lagrangian, based solely on classical equations, and demonstrates its application to systems with friction and other models.

Contribution

The paper presents the first functional integral formulation for non-Lagrangian systems, avoiding ambiguities of traditional methods and extending quantum mechanics to broader classes of dissipative systems.

Findings

Successfully applied to systems with power-law friction

Compared results with existing models like Caldirola-Kanai and Kostin

Discussed relations to Caldeira-Leggett and Feynman-Vernon approaches

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.