Integration Theory for Kinks and Sphalerons in One Dimension

2023/08/28 by Manton, N. S. · 3 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2308.14453

Abstract

The static kink, sphaleron and kink chain solutions for a single scalar field ϕ in one spatial dimension are reconsidered. By integration of the Euler--Lagrange equation, or through the Bogomolny argument, one finds that each of these solutions obeys a first-order field equation, an autonomous ODE that can always be formally integrated. We distinguish the BPS case, where the required integral is along a contour in the ϕ-plane, from the semi-BPS case, where the integral is along a contour in the Riemann surface double-covering the ϕ-plane, and is generally more complicated.

Cited by

• Exact BPS double-kinks in generalized ϕ⁴, ϕ⁶ and sine-Gordon models
• Long-time behaviour of sphalerons in ϕ⁴ models with a false vacuum
• Instability of sphalerons in ϕ⁴ models with a false vacuum

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