期刊
PHYSICAL REVIEW D
卷 103, 期 2, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.103.025024
关键词
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资金
- U.K. Science and Technology Facilities Council [ST/P000681/1]
- NCN, Poland [2019/03/X/ST2/01690, 2019/35/B/ST2/00059]
- Polish National Science Centre
- NCN [2019/35/B/ST2/00059]
- STFC [ST/P000681/1] Funding Source: UKRI
This paper revisits the finite-dimensional collective coordinate manifolds for kinks and antikinks in phi(4) theory and sine-Gordon theory, where the confined field theory Lagrangian on moduli space defines a reduced Lagrangian, and moduli spaces should be metrically complete or have infinite potential on their boundary.
Moduli spaces-finite-dimensional, collective coordinate manifolds-for kinks and antikinks in phi(4) theory and sine-Gordon theory are reconsidered. The field theory Lagrangian restricted to moduli space defines a reduced Lagrangian, combining a potential with a kinetic term that can be interpreted as a Riemannian metric on moduli space. Moduli spaces should be metrically complete, or have an infinite potential on their boundary. Examples are constructed for both kink-antikink and kink-antikink-kink configurations. The naive position coordinates of the kinks and antikinks sometimes need to be extended from real to imaginary values, although the field remains real. The previously discussed null-vector problem for the shape modes of phi(4) kinks is resolved by a better coordinate choice. In sine-Gordon theory, moduli spaces can be constructed using exact solutions at the critical energy separating scattering and breather (or wobble) solutions; here, energy conservation relates the metric and potential. The reduced dynamics on these moduli spaces accurately reproduces properties of the exact solutions over a range of energies.
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