Dimensional crossover in non-relativistic effective field theory*

In our project, we consider two-body isotropic scattering with an arbitrary finite-range potential—confined by anisotropic harmonic traps—studied using non-relativistic effective field theory. Compactification from three spatial dimensions to a plane and a line, and from a plane to a line are considered and general relations among effective-range parameters in the various dimensions are obtained, confirming known results and providing several new relations. This is an extension of our previous work which considered toroidal compactification. The implications of this research allow for the calculation of thermodynamic properties of Bosonic gas systems in lower dimensions when only properties of three dimensions can be measured experimentally. Moreover, the calculation will also shed light about the fundamental characteristics and dynamics of an arbitrary low-energy Bose gas system when dimensionally interpolated.