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Abstract

Neutrino oscillations are a phenomenon beyond the Standard Model that is very well established experimentally. They were observed in the atmospheric, solar, accelerator and reactor neutrino experiments. This is an important fact for modern physics, since it demonstrates that neutrinos are massive. In the present work we describe neutrino oscillations in non-uniform matter, using an approach based on Quantum Field Theory, in which neutrino production, propagation and detection are considered as a single process. In this approach neutrinos are described through propagators connecting the production and detection vertices in a general Feynman diagram. In our treatment the information about neutrino-matter interaction is contained in the neutrino propagator through an effective matter potential. We present a way to define a meaningful oscillation probability using the Feynman rules and experimental considerations. From this quantity we derive the amplitude for the oscillation process and determine under which conditions it coincides with the result predicted by the standard approach, where the amplitude is found from a Schrödinger-like evolution equation. To illustrate the approximations used in the calculations we present an example of two-flavour oscillations in the adiabatic limit.