A Mathematical and Physical Analysis On the Origin of Objects (or Matters) in Space (3)
3.2 Topological Defects as Precursors of Matter
\[\oint_C \nabla \theta \cdot d\mathbf{l} = 2\pi n\]
3.3 Possible Pathways for Topological Phase Transitions to Generate Matter
2) Vortex interactions and composite structures:
- Multiple vortices can form knots through intertwining and linking, corresponding to different particle types [4];
- Vibrational modes of vortex rings can be interpreted as internal degrees of freedom (e.g., electric charge, color charge);
- Vortex dynamics described by topological current equations may be isomorphic to Yang-Mills equations.
4. Interface with Existing Physical Theories and Predictions
4.1 Correspondence with Quantum Field Theory
1) The vortex core scale may correspond to the Planck scale or some equivalent cutoff scale;
3) The vortex excitation spectrum might reproduce the Standard Model particle spectrum [5].
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