Why use coherent state path integral? What is its motivation or goal? In almost all textbooks of quantum field theory for high energy, they insert the position and momentum eigenstate to formulate the path integral. While in condensed matter field theory, they insert the coherent state to get the path integral. What's the motivation or goal to use the latter instead of the former?
 A: The coherent state path integral is basically a recipe for converting a Hamiltonian into a Lagrangian.  In condensed matter, we often start with a "microscopic" Hamiltonian description of a material at the level of individual atoms/electrons, and want to convert that into a Lagrangian so that we can more easily do QFT.  In high energy, it's usually easier to go directly to the Lagrangian description right away, and it's rarely necessary to consider a Hamiltonian more complicated than that of a free particle, or one experiencing some generic, unspecified potential $V(\varphi)$.
A: In condensed matter, we are usually interested in systems with many particles and their interactions. Thus coherent state representation of the path integral is just a many-body generalization of the single-particle path integral for the case of systems that are described by Hamiltonians with terms consisting of creation and annihilation operators, i.e. ($a$, $a^{\dagger}$ instead of $x$ and $p$ of a single particle).
