Lagrangian, the analogue of the Lagrange function of a classical physical field in quantum field theory (QFT). In QFT the functions describing the field are replaced by the corresponding operators, so that the Lagrangian is an operator. Its form is connected with the Lagrange function for the classical field by the correspondence principle. The Lagrangian completely determines the theory, that is, it makes it possible to find the equation for interacting quantum fields and, in principle, to determine the scattering matrix. The Lagrangian approach is more general than the Hamiltonian one (see Hamiltonian); in particular it holds in non-local field theories as well, in which the Hamiltonian method is not applicable. The term “Lagrangian” is sometimes applied also to the Lagrange function for classical fields.