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Standard arguments state that Bose Einstein condensation (BEC) cannot occurin dimensions lower than three in the thermodynamic limit as the expressionsfor the number of bosons in the excited states are unbounded. These argumentsimply that the number density is infinite, which is an extraordinary condition.As an alternative to this pedagogy, we explore the use of regularizationtechniques to show that the number density of bosons in the excited state isfinite in two and one dimensions at low temperatures, making it possible tohave a BEC transition in the thermodynamic limit. We suggest creating atwo-dimensional optical traps of increasing sizes to test this hypothesis asthe thermodynamic limit is approached.

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