**Are there some articles or books in which Quantum Field Theory is treated systematically using a least action principle?** I don't mean the path integral formalism, but a "true", "classical" Lagrangian formulation, and the dynamics being obtained by minimizing the action.

For example, the Klein-Gordon and Dirac equations have Lagrangian formulations, as well as the nonrelativistic Schrödinger equation, including for more particles, for example for two particles we have the following Lagrangian

\[\mathcal L(x_1,x_2,t)=\hbar Im\{\psi^\ast\frac{\partial \psi}{\partial t}\}+\frac{\hbar^2}{2m_1}\nabla_1\psi^\ast\cdot\nabla_1\psi + \frac{\hbar^2}{2m_2}\nabla_2\psi^\ast\cdot\nabla_2\psi + V(x_1,x_2)\psi^\ast\psi\]

I imagine that we can include more particles, and linear combinations of states of different numbers of particles, so I see no reason why the same can't work for a variable number of particles. Also, QFT being a dynamical system, quantum as it is, I still see no reason why it can't be described as minimizing an action.

But in all references I found, including by searching online, one moves to antiparticles and creation and annihilation operators, and usually what's called Lagrangian or variational formulation is actually Feynman's path integral approach, which uses the action in a different way than the least action principle. I am also aware of the question https://physicsoverflow.org/20612/quantum-mechanics-as-classical-field-theory?show=20612 and the answers, but unless I missed something for the references from the answers, they are all about path integrals. Also, the equation written above is from this article http://www.scottforth.com/publications/2002_AmJPhys_Styer%20et%20al.pdf section G, and they give as reference for QFT Itzykson and Zuber's Quantum Field Theory, yet there again I find the path integral formulation.

Maybe it doesn't work and it turns out that the so-called second quantization is needed, and some probabilistic interpretation, but I wonder if there's some literature in which it is treated systematically, and shown why is or is not equivalent to the usual formulations.