Multi-particle States from the Effective Action for Local Composite Operators: Anharmonic Oscillator

TL;DR

This paper derives the effective action for a local composite operator in a scalar quantum field theory with $\

Contribution

It provides a five-loop calculation of the effective action for composite operators in an anharmonic oscillator model, improving spectrum accuracy.

Findings

Ground state energy matches the exact spectrum better than perturbation theory.

Effective potential and Green's functions are explicitly derived.

Results demonstrate the effectiveness of the 2PPI expansion in quantum mechanics.

Abstract

The effective action for the local composite operator $\Phi^2(x)$ in the scalar quantum field theory with $\lambda\Phi^4$ interaction is obtained in the expansion in two-particle-point-irreducible (2PPI) diagrams up to five-loops. The effective potential and 2-point Green's functions for elementary and composite fields are derived. The ground state energy as well as one- and two-particle excitations are calculated for space-time dimension $n=1$, when the theory is equivalent to the quantum mechanics of an anharmonic oscillator. The agreement with the exact spectrum of the oscillator is much better than that obtained within the perturbation theory.