The original TeX representation of the formula was written by Thomas D. Gutierrez in 1999 [1]. It was discussed many times on HN, initially in 2016 a day after the post of this article on symmetrymagazine [2].
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?
In QFT, the Lagrangian is usually the form that's most useful, as this is what you use to calculate scattering amplitudes for processes. The Feynman rules for scattering processes come from the path integral formulation, which uses the "action", a quantity that's the integral of the Lagrangian.
My context is I'm (slowly) writing a quantum field simulator as a hobby. I've done this before for EM fields only, and am familiar with how to directly apply Maxwell's equations as a simulation. But the Lagrangian I have no clue how to directly utilize in a simulation. Hence my search for field evolution equations.
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.