Sorry for a naive question. In EM textbook and QM path integral textbook, the action and Lagrangian in electromagnetic interaction are S = L dt = e(\phi – A v) dt ---equ.(1) But in QFT textbook, the action and Lagrangian density are S = L d^4x = A J d^4x ---equ.(2) As I understand, in equ.(2), J = \rho U = \rho \gamma V In which \rho is density, U is the 4-velocity=dx/d\tau, and V is the common velocity=dx/dt, \gamma is \sqrt (1-v^2/c^2). So equ.(2) will have a factor of \gamma, but equ.(1) does not have. So where is my mistake?