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

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

1995-12-15

arxiv.org/abs/hep-th/9512113v2

Annals Phys. 249 (1996) 367-379

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, plain Latex, 4 tared, compressed and uuencoded Postscript figures

Scientific paper

10.1006/aphy.1996.0076

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.

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