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Rotational and Translational Characteristics of Topological Vortices and Antivortices Based on Perspectives from Loops and Knots (1)

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Posted 2025-10-20 05:09:02

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Based on Topological Vortex Theory (TVT), this paper systematically investigates the fundamental characteristics of vortices and their corresponding antivortices in rotational and translational motion. By introducing topological structures such as loops and knots, the dynamical behaviors of vortex-antivortex pairs, including their interaction mechanisms, structural stability, and their impact on spatiotemporal topology, are analyzed. The results indicate that the difference in the rotational direction between vortices and antivortices can induce a rich variety of topological phase transitions, while their translational motion reveals propagation and evolution characteristics through knot theory. These findings not only deepen the theoretical understanding of topological defect dynamics but also provide a theoretical basis for applications in optical vortices, quantum condensed matter physics, and related cutting-edge fields.

Keywords: Topological Vortex Theory; Vortex-Antivortex Pair; Rotational Characteristics; Translational Characteristics; Loop Structure; Knot Theory

1. Introduction

Topological Vortex Theory (TVT) serves as a fundamental theoretical framework for studying vortex phenomena, typically describing the formation and evolution of vortices using order parameter fields and free energy functionals. As a typical topological defect, the core feature of a vortex is the presence of a phase singularity; the antivortex, as its topological conjugate, exhibits significantly different physical behaviors in rotational and translational motion. Loops and knots, as important tools for characterizing topological invariants, provide key theoretical support for understanding the dynamics of vortex-antivortex pairs. For instance, the phase singularity structure in optical vortices can be described by knot theory to understand its propagation behavior, while vortex-antivortex pairs in quantum condensed matter systems can be analyzed for stability via loop structures. This paper aims to systematically explore the characteristic features of vortices and antivortices during rotation and translation, with a focus on analyzing their intrinsic relationship with topological structures like loops and knots.

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