Abstract
We discuss a number of interesting aspects of nonlinear supersymmetry in the general context of predicting the main candidates for beyond the Standard Model physics or understanding the dynamical behavior of strongly interacting quantum systems where the usual theoretical tools, such as perturbation theory are not applicable anymore. We focus on the relation between nonlinear supersymmetry as a natural generalization of linear supersymmetry and generalized statistics, drawing attention to exotic properties related to quantum anomalies, the emergence of hidden symmetries and nonlinear superconformal symmetry. We discuss distinctive properties of nonlinear supersymmetry and nonlinear superconformal symmetry and investigate one-dimensional quantized supersymmetric systems exhibiting nonlinear features. These properties provide a natural explanation for exotic features and anomalous dynamics in quantum systems, leading to various models and mechanisms in field theory, nonlinear wave physics, cosmology, and condensed matter physics.
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