The Auxiliary Field Method as a Powerful Tool for Nonperturbative Study

Details The Auxiliary Field Method as a Powerful Tool for Nonperturbative Study The Auxiliary Field Method as a Powerful Tool for Nonperturbative Study

1998-09-19

arxiv.org/abs/hep-th/9809141v1

Phys.Rev. D59 (1999) 085002

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, 5 figures

Scientific paper

10.1103/PhysRevD.59.085002

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.

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