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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.
