Approximate determination of the mass gap in quantum field theory using the method of finite elements

In a previous paper on the method of finite elements we developed an extremely simple procedure for obtaining the approximate energy levels of a quantum-mechanical system. This procedure is purely analytical rather than numerical and it gives accurate results. In this paper we apply this same procedure to self-interacting, two-dimensional, scalar quantum field theory. Specifically, we calculate the mass renormalization for the (${\phi }^{2N}$ ${)}_2$ and the sine-Gordon field theories.