Discussion on Lorentz Invariance Violation of Non-commutative Field Theory and Neutrino Oscillation

Depending on deformed canonical anti-commutation relations, massless neutrino oscillation based on Lorentz invariance violation in non-commutative field theory is discussed. It is found that the previous studies about massless neutrino oscillation within deformed canonical anti-commutation relations should satisfy the condition of new Moyal product and new non standard commutation relations. Furthermore, comparing the Lorentz Invariant Violation parameters $\mathit{A}$ in the previous studies with new Moyal product and new non standard commutation relations, we find that the orders of magnitude of non-commutative parameters (Lorentz invariant Violation parameters $\mathit{A}$) is not self-consistent. This inconsistency means that the previous studies of Lorentz invariance violation in non-commutative field theory may not naturally explain massless neutrino oscillation. In other words, it should be impossible to explain neutrino oscillation by Lorentz invariance violation in non-commutative field theory. This conclusion is supported by the latest atmospheric neutrinos experimental results from the Super-Kamiokande Collaboration, which show that no evidence of Lorentz invariance violation on atmospheric neutrinos was observed.