Integral for Nonrelativistic Quantum Electrodynamics

Abstract: The Feynman path integral for nonrelativistic quantum electrodynamics is studied mathematically of a standard model in physics, where the electromagnetic potential is assumed to be periodic with respect to a large box and quantized thorough its Fourier coefficients. In physics, the Feynman path integral for nonrelativistic quantum electrodynamics is defined very formally. For example, as is often seen, even independent variables are not so clear. First, the Feynman path integral is defined rigorously under the constraints familiar in physics. Secondly, the Feynman path integral is also defined rigorously without the constraints, which is stated in Feynman and Hibbs’ book without any comments. So, our definition may be completely new. Thirdly, the vacuum and the state of photons of momentums and polarization states are expressed by means of concrete functions of variables consisting of the Fourier coefficients of the electromagnetic potential. Our results above have many applications as is seen in Feynman and Hibbs’ book, though the