BPS states in interacting field theory refer to specific solutions that preserve a certain amount of supersymmetry. To obtain BPS states, one must analyze the action of the theory and identify the conditions under which these states exist, typically involving first-order differential equations derived from the equations of motion. The significance of BPS states lies in their stability and the preservation of certain quantum numbers, which can be crucial for understanding the non-perturbative aspects of the theory. For detailed calculations and theoretical background, refer to page 441 of "The Quantum Theory of Fields II" by Steven Weinberg.
PREREQUISITESThe discussion is beneficial for theoretical physicists, graduate students in quantum field theory, and researchers interested in supersymmetry and soliton solutions.