A Novel Non perturbative Self-consistent and General Approximation Method in Quantum Theory

TL;DR

This paper introduces a new non-perturbative, self-consistent approximation method for quantum systems that is systematically improvable and applicable across various interaction strengths, improving upon existing approximation techniques.

Contribution

The paper presents a novel approximation scheme that overcomes limitations of traditional methods, applicable to diverse interacting quantum systems with promising potential for broad applications.

Findings

Successfully applied to anharmonic and double-well oscillators

Yields results consistent with supersymmetry predictions

Provides insights into vacuum structure and stability

Abstract

A new method of approximation scheme with potential application to a general interacting quantum system is presented. The method is non-perturbative, self- consistent, systematically improvable and uniformly applicable for arbitrary strength of interaction. It thus overcomes the various limitations of the exsting methods such as the perturbation theory, the variational method, the WKBJ method and other approximation schemes. The current method has been successfully applied to a variety of interacting systems including the anharmonic/ double-well oscillators (with quartic-, sextic- and octic couplings) and the scalar field theory with quartic-coupling in the symmetric phase. The method yields important insight in to the structure and stability of the interacting-vacuum of the theory. The results are in good agreement with the exact predictions of supersymmetry where ever applicable. Possible further applications in the areas of quantum statistics, finite temperature field theory, condensed matter physics etc are also discussed.