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The recent experimental progress in laser cooling and trapping of neutral atoms brings the atomic samples into the ultracold regime where the bosonic atoms and fermionic atoms are expected to have different dynamic behaviours in the laser fields. In this paper we systematically introduce the theoretical study of interaction of an ultracold atomic ensemble with a light wave in the frame of a vector quantum field theory. The many-body quantum correlation in the ultracold regime of atom optics is studied in terms of vector quantum field theory. A general formalism of nonlinear atom optics for a coherent atomic beam is developed.

Vector Quantum Field Theory of Atoms: Nonlinear Atom Optics and Bose - Einstein Condensate