Well-Defined Quantum Soliton Masses Without Supersymmetry

Abstract

22 years ago, Rebhan and van Nieuwenhuizen showed that loop corrections to the mass of a quantum soliton depend on a choice of matching condition for the regulators of the vacuum and one-soliton sector Hamiltonians. In supersymmetric theories, regulators which preserve supersymmetry yield the correct quantum corrections, as these are dictated by supersymmetry. However, in a general theory it is not known which matching condition yields the correct mass. We use the leading term in the operator that creates the soliton to construct the regulated one-soliton sector Hamiltonian from that of the vacuum sector, providing the correct matching condition. As an application, we derive a simple formula for the one-loop mass of a kink in a large class of 1+1 dimensional scalar field theories and also, at one loop, we diagonalize the Hamiltonian which describes the kink excitations.

arXiv comment10 pages, no figures, v2 typo fixed

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Cited by in corpus (13)

• Two-Loop Scalar Kinks
• Spectral walls in multifield kink dynamics
• Spectral Walls at One Loop
• Normal Ordering Normal Modes
• Excited Kinks as Quantum States
• Accelerating Solitons
• Cut-Off Kinks
• Moving Kinks and Their Wave Packets
• An Alternative to Collective Coordinates
• Constructing Quantum Soliton States Despite Zero Modes
• The ${\varphi }^4$ Kink Mass at Two Loops
• Removing Tadpoles in a Soliton Sector
• Ground States of the ${\varphi }^4$ Double-Well QFT