Comment on ''A path integral leading to higher-order Lagrangians, arXiv:0708.4351 [hep-th]''

TL;DR

This paper critiques a previous work by demonstrating that its effective Lagrangian is inconsistent with the exact Lagrangian, highlighting issues in the path integral method used to eliminate non-auxiliary variables.

Contribution

It identifies and explains the inconsistency in the effective Lagrangian derived using path integral methods, providing clarification on the correct approach.

Findings

The effective Lagrangian in [1] is inconsistent with the exact Lagrangian in [2]

The inconsistency stems from the way path integrals are used to eliminate variables

The paper clarifies the correct method for variable elimination in path integral formulations

Abstract

We show that the ``effective Lagrangian'' constructed in [1] is inconsistent with the exact result for the complete Lagrangian presented in [2]. We trace the origin of the inconsistence to the peculiar way in which the path integral methods are used to eliminate variables that are not auxialiry.