Quantum field theories in particle physics, such as quantum electrodynamics, are usually described in terms of\\ mathcal, and the terms in this form of the Lagrangian translate quickly to the rules used in evaluating Feynman diagrams.
Quantum field theories in particle physics, such as quantum electrodynamics, are usually described in terms of\\ mathcal because quantum fields have a non-trivial distribution in spacetime. An additional benefit is that the terms in this form of the Lagrangian were translated by Feynman to the rules used today in evaluating Feynman diagrams.