Poisson brackets

Poisson brackets are a mathematical tool used in physics, particularly in classical mechanics, to describe how two quantities (like position and momentum) change relative to each other over time. They measure the degree of their interdependence and how the state of a system evolves. If the Poisson bracket between two quantities is zero, it indicates they are compatible or conserved simultaneously. Essentially, Poisson brackets provide a structured way to analyze the dynamics and symmetries within a physical system, helping us understand how different properties influence each other during motion.