These field equations I always see presented as the Lagrangian. But I've had trouble locating any presentation of them as field evolution equations (not sure the right term here, but e.g. how Maxwell's equations are typically presented, as partial differential equations with respect to spacetime dimensions). Deriving this form from the Lagrangian seems a daunting and error-prone task. Does anyone know a reference which presents them in this way?
https://en.wikipedia.org/wiki/Mathematical_formulation_of_th... I think at least provides the field evolution equations for the free fields. But I can't find the equivalent for the interaction terms. E.g. the path integral formation I can only find Lagrangians for.
These field equations I always see presented as the Lagrangian. But I've had trouble locating any presentation of them as field evolution equations (not sure the right term here, but e.g. how Maxwell's equations are typically presented, as partial differential equations with respect to spacetime dimensions). Deriving this form from the Lagrangian seems a daunting and error-prone task. Does anyone know a reference which presents them in this way?
I've had the same question for ages. Shouldn't there be an equation in "Schroedinger form" with some relativistic Hamiltonian?
https://en.wikipedia.org/wiki/Mathematical_formulation_of_th... I think at least provides the field evolution equations for the free fields. But I can't find the equivalent for the interaction terms. E.g. the path integral formation I can only find Lagrangians for.