Wave functionals for field theories and path integrals

A method which allows the calculation of the wave functions of a field theory from the path integral is proposed. I show that the wave function of the ground state is determined by the generating function of the Green functions at equal time. It is shown that there is also a direct connection between the wave function of the ground state (more precisely, the probability of a configuration with a constant field in the ground state) and the theory of the effective potential. This result is further used to exhibit the dependence of the ground state wave function on the anomalous dimensions of the system near criticality. I also show, that the Jastrow wave function is a natural first approximation for all of these systems and give a general prescription for the calculation of correction to the Jastrow form. This formalism is presented within the framework of a field theory of a real scalar field with a global discrete symmetry group ℤ₂, which describes the critical behavior of quantum Ising ferromagnets at zero temperature.