## The Inverse Variational Problem in Classical Mechanics, World Scientific, Singapore

- J. Lopuszański
- 1999

2 Excerpts

- Published 2008

Suppose we have two nonequivalent but s-equivalent Lagrange functions, the question arises: are they both equally well fitted for the Feynman quantization procedure or do they lead to two different quantization schemes. 1. The goal of this note is to exhibit the following problem. It is well known that in the quantization prescription, based on the Feynman “integral over all paths” the classical Lagrange function is used in the exponent of the integrand of the Feynman integral. The physical content of a dynamical system is, however, mainly characterized by the equations of motion of this systems; the Lagrange function, if such one exists at all for these equations, plays a secondary rôle, as there can be many nonequivalent Lagrange functions linked to equations of motion (Euler Lagrange Equations), yielding the same set of solutions so called s-equivalent equations. The question arises: suppose we have two nonequivalent but s-equivalent Lagrange functions, are they both equally well fitted for the Feynman quantization procedure or do they lead to two different quantization schemes. 2. To begin with let us consider the case of one classical particle in a (1+1)-dimensional space-time and the largest set of s-equivalent Lagrange functions, corresponding to the equation of motion of this particle. We do

@inproceedings{Lopuszaski2008MA2,
title={M ay 2 00 0 Some Remarks Concerning the Feynman “ Integral over All Paths ” Method},
author={Jan Lopuszański},
year={2008}
}