Hamiltonian Effective Potential

A Hamiltonian effective potential (the logarithm of the square of the wave functional) is defined and calculated at the tree and one loop levels in a $\phi^4$ scalar field theory. The loop expansion for eigenfunctionals is equivalent to the combination of WKB expansion and an expansion around constant field configurations. The results are compared with those obtained from the Lagrangian effective potential. While at tree level the results from the two methods coincide, at one loop level they differ. Our result at one loop level is that the reflection symmetry is not broken at $m^2\geq0$.