On the possibility of Bose-Einstein condensation in lower dimensions in the thermodynamic limit

Abstract: Standard arguments state that Bose Einstein condensation (BEC) cannot occur in dimensions lower than three in the thermodynamic limit as the expressions for the number of bosons in the excited states are unbounded. These arguments imply that the number density is infinite, which is an extraordinary condition. As an alternative to this pedagogy, we explore the use of regularization techniques to show that the number density of bosons in the excited state is finite in two and one dimensions at low temperatures, making it possible to have a BEC transition in the thermodynamic limit. We suggest creating a two-dimensional optical traps of increasing sizes to test this hypothesis as the thermodynamic limit is approached.