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The origins of neutrino masses is one of the biggest mysteries in modern physics since they are beyond the realm of the Standard Model. As massive particles, neutrinos undergo flavor oscillations throughout their propagation. In this paper we show that when a neutrino oscillates from a flavor state {\alpha} to a flavor state \b{eta}, it follows three possible paths consistent with the Quantum Yang- Baxter Equations. These trajectories define the transition probabilities of the oscillations. Moreover, we define a probability matrix for flavor transitions consistent with the Quantum Yang-Baxter Equations, and estimate the values of the three neutrino mass eigenvalues within the framework of the triangular formulation.
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The cosmological constant is normally introduced as an additional term entering the Einstein–Hilbert (EH) action. In this letter, we demonstrate that, instead, it appears naturally from the standard EH action as an invariant term emerging from spacetime symmetries. We then demonstrate that the same constraint emerging from this invariant suppresses the short wavelength modes and it favors the long wavelength ones. In this way, inside the proposed formulation, the observed value for the vacuum energy density is obtained naturally from the zero-point quantum fluctuations.
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The mutual information method has demonstrated to be very useful for deriving the potential order parameter of a system. Although the method suggests some constraints which help to define this quantity, there is still some freedom in the definition. The method then results inefficient for cases where we have order parameters with a large number of constants in the expansion, which happens when we have many degenerate vacuums. Here, we introduce some additional constraints based on the existence of broken symmetries, which help us to reduce the arbitrariness in the definitions of the order parameter in the proposed mutual information method.
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We demonstrate that the flavor oscillation when a neutrino travels through spacetime, is equivalent to permanent changes on the vacuum state condition perceived by the same particle. This can be visualized via the Quantum Yang Baxter equations (QYBE). From this perspective, the neutrino never breaks the symmetry of the ground state because it never selects an specific vacuum condition. Then naturally the Higgs mechanism cannot be the generator of the neutrino masses. The constraints emerging from this model predict a normal mass hierarchy and some specific values for the mass eigenvalues once we fix the mixing angles. Interestingly, the model suggests that the sum of the mix angles is equal to $\pi/2$.
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We demonstrate that black hole evaporation can be modeled as a process where one symmetry of the system is spontaneously broken continuously. We then identify three free parameters of the system. The sign of one of the free parameters governs whether the particles emitted by the black hole are fermions or bosons. The present model explains why the black hole evaporation process is so universal. Interestingly, this universality emerges naturally inside certain modifications of gravity.
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The Revenue Management (RM) problem in airlines for a fixed capacity, single resource and two classes has been solved before by using a standard formalism. In this paper we propose a model for RM by using the semi-classical approach of the Quantum Harmonic Oscillator. We then extend the model to include external factors affecting the people’s decisions, particularly those where collective decisions emerge.
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It has been claimed in \cite1, that the idea proposed in \cite2 has certain mistakes based on arguments of energy conditions and others. Additionally, some of the key arguments of the paper are criticized. Here we demonstrate that the results obtained in \cite2 are correct and that there is no violation of any energy condition. The statements claimed in \cite1 are based on three things: 1). Misinterpretation of the metric solution. 2). Language issues related to the physical quantities obtained in \cite1, where the authors make wrong interpretations about certain results over the geometry proposed in \cite2. 3). Non-rigorous evaluations of the vacuum condition defined via the result over the Ricci tensor R_\mu\nu=0.