History of variational principles in physics involves integrals over an interval of time and (for fields) extended region of space. Moreover, in the usual formulation of classical action principles, the initial and final states of the system are fixed, e.g., In particular, the fixing of the "final" state appears to give the action principle a teleological character which has been controversial historically. This apparent teleology is eliminated in the quantum mechanical version of the action principle. History of variational principles in physics A variational principle in physics is an alternative method for determining the state or dynamics of a physical system, by identifying it as an
Weak interaction distances, less than the diameter of a proton. It is one of the four known fundamental interactions of nature, alongside the strong interaction, electromagnetism, and gravitation. The Standard Model of particle physics provides a uniform framework for understanding the electromagnetic, weak, and strong interactions. An interaction occurs when two particles, typically but not necessarily half-integer spin fermions, exchange integer-spin, force-carrying bosons. The fermions involved in such exchanges can be either elementary (e.g. electrons or quarks) or composite (e.g. protons or neutrons), although at the deepest levels, all weak interactions ultimately are between elementary particles. In the case of the weak