A comprehensive overview of kaon decays is presented. The standard model predictions are discussed in detail, covering both the underlying short-distance electroweak dynamics and the important interplay of QCD at long distances. Chiral perturbation theory provides a universal framework for treating leptonic, semileptonic, and nonleptonic decays including rare and radiative modes. All allowed decay modes with branching ratios of at least 10-11 are analyzed. Some decays with even smaller rates are also included. Decays that are strictly forbidden in the standard model are not considered in this review. The present experimental status and the prospects for future improvements are reviewed.

Scalar and tensor interactions were once competitors to the now well-established $V-A$ structure of the standard model weak interactions. We revisit these interactions and survey constraints from low-energy probes (neutron, nuclear, and pion decays) as well as collider searches. Currently, the most stringent limit on scalar and tensor interactions arise from $0^{+}\to 0^{+}$ nuclear decays and the radiative pion decay $\pi \to e\nu \gamma$, respectively. For the future, we find that upcoming neutron beta decay and LHC measurements will compete in setting the most stringent bounds. For neutron beta decay, we demonstrate the importance of lattice computations of the neutron-to-proton matrix elements to setting limits on these interactions, and provide the first lattice estimate of the scalar charge and a new average of existing results for the tensor charge. Data taken at the LHC is currently probing these interactions at the ${10}^{-2}$ level (relative to the standard weak interactions), with the potential to reach the $\lesssim {10}^{-3}$ level. We show that, with some theoretical assumptions, the discovery of a charged spin-0 resonance decaying to an electron and missing energy implies a lower limit on the strength of scalar interactions probed at low energy.

We present a formulation of the quantum kinetic equations (QKEs), which govern the evolution of neutrino flavor at high density and temperature. Here, the structure of the QKEs is derived from the ground up, using fundamental neutrino interactions and quantum field theory. We show that the resulting QKEs describe coherent flavor evolution with an effective mass when inelastic scattering is negligible. The QKEs also contain a collision term. This term can reduce to the collision term in the Boltzmann equation when scattering is dominant and the neutrino effective masses and density matrices become diagonal in the interaction basis. We also find that the QKEs include equations of motion for a new dynamical quantity related to neutrino spin. This quantity decouples from the equations of motion for the density matrices at low densities or in isotropic conditions. However, the spin equations of motion allow for the possibility of coherent transformation between neutrinos and antineutrinos at high densities and in the presence of anisotropy. Although the requisite conditions for this exist in the core collapse supernova and compact object merger environments, it is likely that only a self-consistent incorporation of the QKEs in a sufficiently realistic model could establish whether or not significant neutrino-antineutrino conversion occurs.