Topological quantum phases for an electron or system of electrons in braided energy field fluid configurations

The energy eigenvalues of ‘quantum fluctuations’ as a manifestation of ‘quantum phases’ for electrons with stretching, twisting, and twigging in topological space-time we obtained. Electrons are treated as energy field fluids in braided configurations instead of point particles. The quantization of events in ‘quasi–particles or time crystals occurs because of the stretching of eigenfunctions, which are manifestations of twisting and twigging with relativistic quantum electrodynamics (QED) behavior. The mathematical expression or energy eigenvalues are ±ℏt_(n_f ) υα(t_(n_f )), where ± signs indicate forward and backward helical responses of “quantum phases”, 0.1 ≤ n_f≤ 0.9,0.17≤α(t_(n_f ))≤1.53 rad and υ the frequency at Twiggs with whirlpools and potential barriers.