2019/05/08 by Wen-Du Li, Li, Wen-Du, Wu-Sheng Dai +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #FOS: Physical sciences #General Physics (physics.gen-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1905.06805
openalex publication_date 2019/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that there exists a duality among fields. If a field is dual to another field, the solution of the field can be obtained from the dual field by the duality transformation. We give a general result on the dual fields. Different fields may have different numbers of dual fields, e.g., the free field and the ϕ4-field are self-dual, the ϕn-field has one dual field, a field with an n-term polynomial potential has n+1 dual fields, and a field with a nonpolynomial potential may have infinite number of dual fields. All fields which are dual to each other form a duality family. This implies that the field can be classified in the sense of duality, or, the duality family defines a duality class. Based on the duality relation, we can construct a high-efficiency approach for seeking the solution of field equations: solving one field in the duality family, all solutions of other fields in the family are obtained immediately by the duality transformation. As examples, we consider some ϕn-fields, general polynomial-potential fields, and the sine-Gordon field.