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Advances in High Energy Physics
Volume 2013 (2013), Article ID 304980, 18 pages
Research Article

Cyclically Deformed Defects and Topological Mass Constraints

1Departamento de Física, Universidade Federal de São Carlos, P.O. Box 676, 13565-905 São Carlos, SP, Brazil
2Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170 Santo André, SP, Brazil

Received 6 December 2012; Accepted 27 February 2013

Academic Editor: Ira Rothstein

Copyright © 2013 A. E. Bernardini and Roldão da Rocha. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A systematic procedure for obtaining defect structures through cyclic deformation chains is introduced and explored in detail. The procedure outlines a set of rules for analytically constructing constraint equations that involve the finite localized energy of cyclically generated defects. The idea of obtaining cyclically deformed defects concerns the possibility of regenerating a primitive (departing) defect structure through successive, unidirectional, and eventually irreversible, deformation processes. Our technique is applied on kink-like and lump-like solutions in models described by a single real scalar field such that extensions to quantum mechanics follow the usual theory of deformed defects. The preliminary results show that the cyclic device supports simultaneously kink-like and lump-like defects into 3- and 4-cyclic deformation chains with topological mass values closed by trigonometric and hyperbolic deformations. In a straightforward generalization, results concerning the analytical calculation of N-cyclic deformations are obtained, and lessons regarding extensions from more elaborated primitive defects are depicted.