Document Type : Regular article

Author

• Chen-Te Ma

Asia Center for Theoretical Physics

Abstract

The perturbation method is an approximation scheme with a solvable leading order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part by using all diagonal elements for a Fock state. We consider the harmonic oscillator with the interacting term, λ₁x⁴/6 + λ₂x⁶/120, where λ₁ and λ₂ are coupling constants, and x  is the position operator. The spectrum shows a quantitative result from the second-order, less than 1 percent error, compared to a numerical solution when turning off the λ₂. When we turn on the λ₂, more deviation occurs, but the error is still less than 2 percent. We show a quantitative result beyond a weak-coupling region. Our study should provide interest in the holographic principle and strongly coupled boundary theory.

Keywords

• Fock State
• Harmonic Oscillator
• QFT
• Hamiltonian
• Strongly Coupled Physics

Main Subjects

• Physics