Duality family of scalar field
Abstract
We show that there exists a duality family of self-interacting massive scalar fields. The scalar field in a duality family are related by a duality transformation. Such a duality of scalar fields is a field version of the Newton-Hooke duality in classical mechanics. The duality transformation preserves the type of the field equation: transforming a Klein-Gordon type equation to another Klein-Gordon type equation with a different self-interacting potential. Once a field in a duality family is solved, all other family members are solved by the transformation. That is, a series of exactly solvable models can be constructed from one exactly solvable model. The dual field of the power-interaction field, the sine-Gordon field, etc., are considered. Moreover, as a comparison, we show an analogue of the duality in classical and quantum mechanics.
Keywords
Cite
@article{arxiv.1909.11659,
title = {Duality family of scalar field},
author = {Wen-Du Li and Wu-Sheng Dai},
journal= {arXiv preprint arXiv:1909.11659},
year = {2021}
}