Equivalence of Constrained Models

TL;DR

This paper compares two constrained scalar models, showing they appear equivalent in a graphical path integral expansion but differ dynamically when quantized via Dirac's method.

Contribution

It reveals the discrepancy between graphical path integral equivalence and dynamical differences in quantization of constrained models.

Findings

Graphical path integral suggests equivalence of models.

Dynamical analysis via Dirac quantization shows differences.

Highlights importance of quantization method in model equivalence.

Abstract

We study two constrained scalar models. While there seems to be equivalence when the partially integrated Feynman path integral is expanded graphically, the dynamical behaviour of the two models are different when quantization is done using Dirac constraint analysis.