Adaptive Perturbation Theory: Quantum Mechanics and Field Theory

TL;DR

Adaptive perturbation theory offers a novel approach to compute eigenvalues and eigenstates of complex quantum Hamiltonians by decomposing them to extract non-perturbative effects, applicable to quantum mechanics and field theory.

Contribution

The paper introduces adaptive perturbation theory, a new method that captures non-perturbative behavior exactly, extending perturbative techniques to previously intractable quantum systems.

Findings

Successfully applied to anharmonic oscillator

Effectively models tunneling between minima

Non-perturbatively extracts mass, wavefunction, and coupling constants

Abstract

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, $H$, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly. In this talk I will introduce the method in the context of the pure anharmonic oscillator and then apply it to the case of tunneling between symmetric minima. After that, I will show how this method can be applied to field theory. In that discussion I will show how one can non-perturbatively extract the structure of mass, wavefunction and coupling constant