We consider the nonrelativistic four-boson system with short-range forces and large scattering length in an effective quantum mechanics approach. We construct the effective interaction potential at leading order in the large scattering length and compute the four-body binding energies using the Yakubovsky equations. Cutoff independence of the four-body binding energies does not require the introduction of a four-body force. This suggests that two- and three-body interactions are sufficient to renormalize the four-body system. We apply the equations to
4He atoms and calculate the binding energy of the
4He tetramer. We observe a correlation between the trimer and tetramer binding energies similar to the Tjon line in nuclear physics. Over the range of binding energies relevant to
4He atoms, the correlation is approximately linear.
We discuss the application of an effective theory with contact interactions to the non-relativistic four-body system with short-range interactions. We have computed the binding energies of the 4He tetramer and the alpha-particle. A well-known linear correlation between three- and four-body binding energies can be understood as a result of the absence of a four-body force at leading order within this framework. Further, we give results for the binding energies of the four-boson system in two spatial dimensions.