Collective Coordinate Methods and Their Applicability to $\varphi^4$ Models

Herbert Weigel

doi:10.1007/978-3-030-11839-6_3

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arXiv · 1809.03772

Collective Coordinate Methods and Their Applicability to $\varphi^4$ Models

Herbert Weigel

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Abstract

Collective coordinate methods are frequently applied to study dynamical properties of solitons. These methods simplify the field equations - typically partial differential equations - to ordinary differential equations for selected excitations. More importantly though, collective coordinates provide a practical means to focus on particular modes of otherwise complicated dynamical processes. We review the application of collective coordinate methods in the analysis of the kink-antikink interaction within the $\varphi^4$ soliton model and illuminate discrepancies between these methods and the exact results from the field equations.

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Herbert Weigel. 2018-09-11. Collective Coordinate Methods and Their Applicability to $\varphi^4$ Models. https://doi.org/10.1007/978-3-030-11839-6_3

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