Higher-Derivative Models in Contemporary Field Theory

We review and contextualize higher-derivative (HD) models in field theory, including Bopp-Podolsky, Lee-Wick, Pais-Uhlenbeck and HD Klein-Gordon generalizations, while discussing their roles within recent new physics proposals. We present a consistent parametrized family of higher-order generalizations for the Klein-Gordon equation with their corresponding HD actions, illustrate the BRST quantization of the Pais-Uhlenbeck oscillator and discuss the constrained dynamics evolution and canonical quantization of the Bopp-Podolsky model. We show that, through the introduction of higher-derivatives, it is possible to generate massive modes for the gauge fields without breaking their natural local invariance. We propose a consistent reduction of order for higher-derivative models to improve physics interpretation, exemplified in the reduced-order-Bopp-Podolsky model.