The Auxiliary Field Method as a Powerful Tool for Nonperturbative Study

TL;DR

The paper demonstrates that the auxiliary field method, especially with higher loop calculations, effectively provides nonperturbative insights into quantum mechanical systems like the Anharmonic Oscillator and Double-Well potentials, with varying accuracy depending on coupling strength.

Contribution

It shows the effectiveness and limitations of the auxiliary field method with loop-expansion in nonperturbative quantum mechanics analysis.

Findings

Higher loop calculations improve accuracy in weak coupling regions.

2-loop approximation is insufficient for Double-Well potential.

Method's accuracy decreases in strong coupling regions.

Abstract

The auxiliary field method, defined through introducing an auxiliary (also called as the Hubbard-Stratonovich or the Mean-) field and utilizing a loop-expansion, gives an excellent result for a wide range of a coupling constant. The analysis is made for Anharmonic-Oscillator and Double-Well examples in 0-(a simple integral) and 1-(quantum mechanics)dimension. It is shown that the result becomes more and more accurate by taking a higher loop into account in a weak coupling region, however, it is not the case in a strong coupling region. The 2-loop approximation is shown to be still insufficient for the Double-Well case in quantum mechanics.