Perturbative and nonperturbative aspects of neutrino oscillations in quantum field theory

In this work, we present a comprehensive and pedagogical review of two quantum field theoretical approaches to neutrino flavor mixing and oscillations: the nonperturbative flavor Fock space formalism and the perturbative interaction picture framework. Starting from a minimally extended Standard Model, where neutrino masses and mixing are treated analogously to the quark sector, we derive the explicit form of leptonic flavor charges from the charged-current Lagrangian in the spontaneously broken phase. We present the standard quantum mechanical treatment of neutrino oscillations and an alternative derivation based on the first-quantized Dirac equation. We then review the construction of the flavor Fock space, in which flavor states emerge as eigenstates of the flavor charges, and show how oscillation probabilities can be computed both from charge and current expectation values and from Green’s functions. The nontrivial vacuum structure associated with this approach leads to key results such as the conservation of lepton number at tree level and a rigorous derivation of the time–energy uncertainty relation in neutrino oscillations. We also discuss the extension to the three-flavor case and the entangled nature of flavor states. In parallel, we explore a perturbative approach that treats flavor mixing as an interaction. Starting from simple quantum mechanical models and extending to bosonic field theories, we show how neutrino oscillation probabilities can be derived via Dyson expansion in the interaction picture. Remarkably, this method reproduces the same oscillation formulas as the nonperturbative approach, within the expected limits. We emphasize the necessity of working at finite time, rather than in the asymptotic S-matrix framework. Our analysis highlights the conceptual and structural unity of these approaches and offers a solid framework for further developments in the field of neutrino physics.