Variational method for field theories on the lattice and the spectrum of theφ4theory in 1+1 dimensions

An approximation technique to construct the low-lying energy eigenstates of any bosonic field theory on the lattice is proposed. It is based on the SLAC blocking method, after performing a finite-spin approximation to the individual degrees of freedom of the problem. General expressions for any polynomial self-interacting theory are given. Numerical results for ${\phi }^2$ and ${\phi }^4$ theories in 1+1 dimensions are offered; they exhibit a fast convergence rate. The complete low-lying energy spectrum of the ${\phi }^4$ theory in 1+1 dimensions is calculated.