Some Remarks Concerning the Feynman "Integral over All Paths" Method

TL;DR

This paper discusses the implications of using different but s-equivalent Lagrangian functions in Feynman quantization, questioning whether they produce identical quantum theories or different schemes.

Contribution

It analyzes the impact of choosing nonequivalent Lagrangians on the Feynman path integral quantization process.

Findings

Different s-equivalent Lagrangians may lead to distinct quantization schemes.

The choice of Lagrangian affects the resulting quantum theory.

The paper clarifies conditions under which different Lagrangians yield equivalent quantizations.

Abstract

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.