Gauge Independence of the Lagrangian Path Integral in a Higher-Order Formalism

TL;DR

This paper introduces a gauge-invariant Lagrangian path integral framework using a higher-order Δ-operator, ensuring independence from gauge-fixing choices without variable changes.

Contribution

It presents a novel gauge-invariant path integral formulation based on a symmetric higher-order Δ-operator, avoiding explicit variable transformations.

Findings

Path integral is gauge-independent

No change of variables needed for gauge independence

Framework applies to higher-order gauge symmetries

Abstract

We propose a Lagrangian path integral based on gauge symmetries generated by a symmetric higher-order $\Delta$-operator, and demonstrate that this path integral is independent of the chosen gauge-fixing function. No explicit change of variables in the functional integral is required to show this.