Some Problems Concerning Interchange of Order of Integration in Functional Integral Formalism of U(1) Gauge Field Theories

TL;DR

This paper demonstrates that exchanging the order of integration in the functional integral formalism of U(1) gauge theories can lead to incorrect results, highlighting the need for careful mathematical treatment.

Contribution

It provides a detailed analysis showing potential errors in formal manipulations within the functional integral approach for U(1) gauge fields.

Findings

Interchanging integration order can produce erroneous results.

Fubini's theorem is crucial for valid integral manipulations.

Careful mathematical analysis is necessary in gauge field theories.

Abstract

We show that in the functional integral formalism of U(1) gauge field theory some formal manipulation such as interchange of order of integration can yield erroneous results. The example studied is analysed by Fubini theorem.