# Scalar and vector Galileons

## TL;DR

Galileons are special fields with actions leading to second-order equations of motion, avoiding classical and quantum pathologies, and are significant in high energy physics and cosmology.

## Contribution

This paper reviews the construction methods for scalar and vector Galileons, highlighting their importance in theoretical physics.

## Key findings

- Galileons ensure second-order equations of motion.
- They help avoid classical and quantum instabilities.
- Applications span high energy physics and cosmology.

## Abstract

An alternative for the construction of fundamental theories is the introduction of Galileons. These are fields whose action leads to non higher than second-order equations of motion. As this is a necessary but not sufficient condition to make the Hamiltonian bounded from below, as long as the action is not degenerate, the Galileon construction is a way to avoid pathologies both at the classical and quantum levels. Galileon actions are, therefore, of great interest in many branches of physics, specially in high energy physics and cosmology. This proceedings contribution presents the generalities of the construction of both scalar and vector Galileons following two different but complimentary routes.