## 1. Introduction

## 2. Four-State Transitions

#### 2.1. Perturbation Induced Transitions between Flavor States

_{I}are real and therefore physically meaningful.

#### 2.2. Flavor State Transitions as Mass State Transitions

## 3. Transitions between Flavor States: Electron Neutrino Disappearance

## 4. Application to Neutrino Oscillation Experiments

## 5. Conclusions

## Funding

## Conflicts of Interest

## Appendix A. The Physical System

**Figure A1.**The Experimental System and Evolution Parameter Clock [10].

## References

- Tanabashi, M.; Hagiwara, K.; Hikasa, K.; Nakamura, K.; Sumino, Y.; Takahashi, F.; Tanaka, J.; Agashe, K.; Aielli, G.; Amsler, C.; et al. Particle Data Group. Available online: http://pdg.lbl.gov/2019/ (accessed on 15 May 2019).
- Aguilar-Arevalo, A.A.; Brown, B.C.; Bugel, L.; Cheng, G.; Conrad, J.M.; Cooper, R.L.; Dharmapalan, R.; Diaz, A.; Djurcic, Z.; Finley, D.A.; et al. Significant Excess of Electronlike Events in the MiniBooNE Short-Baseline Neutrino Experiment. Phys. Rev. Lett.
**2018**, 121, 221801. [Google Scholar] [CrossRef] [PubMed] - Adamson, P.; Anghel, I.; Aurisano, A.; Barr, G.; Bishai, M.; Blake, A.; Bock, G.J.; Bogert, D.; Cao, S.V.; Carroll, T.J.; et al. Search for Sterile Neutrinos in MINOS and MINOS Using a Two-Detector Fit. Phys. Rev. Lett.
**2019**, 122, 091803. [Google Scholar] [CrossRef] [PubMed] - Fanchi, J.R. The Mass Operator and Neutrino Oscillations. Found. Phys.
**1998**, 28, 1521–1528. [Google Scholar] [CrossRef] - Fanchi, J.R. Parametrized Relativistic Dynamical Framework for Neutrino Oscillations. J. Phys. Conf. Ser.
**2017**, 845, 1–13. [Google Scholar] [CrossRef] - Fanchi, J.R. Parametrized Relativistic Quantum Theory; Kluwer: Dordrecht, The Netherlands, 1993. [Google Scholar]
- Fanchi, J.R. Manifestly Covariant Quantum Theory with Invariant Evolution Parameter in Relativistic Dynamics. Found. Phys.
**2011**, 41, 4–32. [Google Scholar] [CrossRef] - Pavšič, M. The Landscape of Theoretical Physics: A Global View; Kluwer: Dordrecht, The Netherlands, 2001. [Google Scholar]
- Horwitz, L.P. Relativistic Quantum Mechanics; Springer: Dordrecht, The Netherlands, 2015. [Google Scholar]
- Fanchi, J.R. The Relativistic Quantum Potential and Non-locality. In Horizons in World Physics 240; Hauppauge: New York, NY, USA, 2003; pp. 117–159. [Google Scholar]
- Fanchi, J.R. Interaction Induced Flavor Oscillations. In Horizons in World Physics 300; Hauppauge: New York, NY, USA, 2019. [Google Scholar]
- Rusov, V.D.; Vlasenko, D.S. Quantization in relativistic classical mechanics: The Stueckelberg equation, neutrino oscillation and large-scale structure of the Universe. J. Phys. Conf. Ser.
**2012**, 361, 1–15. [Google Scholar] [CrossRef]

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