A Non-perturbative General Approximation Scheme (NGAS) for Interacting Quantum Systems with Perturbation Theory for Arbitrary Strength of Interaction

• URL: http://arxiv.org/abs/1909.12508v2
• Date: Wed, 22 Jan 2025 19:46:46 GMT
• Title: A Non-perturbative General Approximation Scheme (NGAS) for Interacting Quantum Systems with Perturbation Theory for Arbitrary Strength of Interaction
• Authors: Bimal P. Mahapatra, Noubihary Pradhan,
• Abstract summary: Scheme is nonperturbative, yet improvable in a new formulation of perturbation theory, designated as mean field theory (T) We apply the scheme to anharmonic interactions in one dimension employing the harmonic-approximation. Results for the QDWO may be contrasted with those from the standard formulation of perturbation theory.
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• Abstract: A non-perturbative general approximation scheme (NGAS) is presented which is potentially applicable for arbitrary strength of interaction in quantum theory. The scheme utilizes an input Hamiltonian, which is exactly solvable. The effects of interaction are incorporated into this input Hamiltonian through a non-linear feedback mechanism by imposing self-consistency conditions. The method is nonperturbative, yet improvable in a new formulation of perturbation theory, designated as: mean field perturbation theory (MFPT). We apply the scheme to anharmonic interactions in one dimension employing the harmonic-approximation and obtain uniformly accurate results by Borel summation, for the quartic-, sextic-, octic-anharmonic oscillators and to the quartic double-well oscillator (QDWO) for {\emph{arbitrary strength of coupling}}. The {\it{flexibility}} of the scheme to the choice of the input is demonstrated by producing results of comparable accuracy by employing the infinite-square Hamiltonian as input. Application to the {\lambda}{\phi}^4-quantum field theory leads to the equivalence of the present method to the Gaussian-effective potential approach in the harmonic approximation. Additionally,however the underlying condensate structure of the effective vacuum is shown to emerge and the instability of the perturbative ground state is established. The results for the QDWO may be contrasted with those from the standard formulation of perturbation theory , where Borel-summation {\it{fails}} for any value of the coupling strength.

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