2024/10/17 by Peng, Feiyu, Shu, Hongfei · 2 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2410.13364
We study the zero-dimensional prototype of the path integrals in quantum mechanics and quantum field theory, with the action S(ϕ)=(σ)/(2)ϕ2+\fracλ4ϕ4. Using the Lefschetz thimble decomposition and the saddle point expansion, we derive multiple asymptotic formal series of the correlation function associated with the perturbative and non-perturbative saddle points. Furthermore, we reconstruct the exact correlation function employing the Borel resummation. We then consider how to truncate the Dyson-Schwinger (DS) equations beginning with the perturbation expansion of the correlation functions, analogous to the one obtained from the Feynmann diagram in higher dimensions. For the case σ<0, we find that although the asymptotic series around the perturbative saddle point is Borel summable, it does not capture the full information. Consequently, contributions from non-perturbative saddle points must be included to ensure a complete truncation procedure.