Functional Integrals

Functional integrals are a mathematical tool used in physics to analyze systems with many possible configurations, such as fields or particles. Instead of summing over a few discrete states, a functional integral sums over all possible functions or paths the system can take. This approach helps in calculating probabilities, energies, and other properties by considering every conceivable way the system can behave. Think of it as averaging over an infinite set of possibilities, allowing physicists to understand complex phenomena like quantum mechanics and field theory in a comprehensive way.