Excited Kinks as Quantum States

Abstract

At one loop, quantum kinks are described by a sum of quantum harmonic oscillator Hamiltonians, and so their spectra are known exactly. We find the first correction beyond one loop to the quantum states corresponding to kinks with an excited bound or unbound normal mode, and also the corresponding two-loop correction to the energy cost of exciting the normal mode. In the case of unbound normal modes, this correction is equal to sum of the corresponding nonrelativistic kinetic energy plus the usual one-loop correction to the mass of the corresponding plane wave in the absence of a kink. We also sketch a diagrammatic method for such calculations.

arXiv comment22+7 pages, 3 embedded figures

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Cited by in corpus (4)

• A Reduced Inner Product for Kink States
• Kink Form Factors
• Removing Tadpoles in a Soliton Sector
• The ${\varphi }^4$ Kink Mass at Two Loops