Multi-particle states from the effective action for local composite operators: Anharmonic oscillator

The effective action for the local composite operator Φ2(x) in the scalar quantum field theory with λΦ4 interaction is obtained in the expansion in two-particle-point-irreducible (2PPI) diagrams up to five-loops. The effective potential and 2-point Green close-quote 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. Copyright copyright 1996 Academic Press, Inc