The problem of gauge invariance and the functional Schroedinger approach

TL;DR

This paper reviews gauge invariance issues in quantum field theory and demonstrates that the functional Schrödinger approach yields gauge-invariant results for the vacuum current, unlike the canonical formulation.

Contribution

It introduces the functional Schrödinger approach as an alternative formulation that resolves gauge invariance issues present in the canonical approach.

Findings

Functional Schrödinger approach produces gauge-invariant vacuum current.

Canonical formulation shows gauge non-invariance in certain calculations.

Alternative formulation may improve consistency in quantum field theory.

Abstract

Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities, such as the vacuum current, are calculated the results are not gauge invariant. The non-gauge invariant terms have to be removed in order to obtain a physically correct result. It has been shown in Ref. [3] and [4] that this problem may be due to a mathematical inconsistency in the canonical formulation of QFT. In this article we will review this previous work and then examine an alternative formulation of QFT called the functional Schroedinger approach. It will be shown that this approach produces different results then the canonical formulation. In particular it will be shown that in the functional Schroedinger approach the vacuum current is gauge invariant.