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

## TL;DR

This paper investigates whether Bose-Einstein condensation can occur in lower dimensions by applying regularization techniques, challenging traditional beliefs that BEC is impossible below three dimensions in the thermodynamic limit.

## Contribution

The authors propose a regularization approach showing finite boson densities in 1D and 2D, suggesting BEC could occur in lower dimensions, and recommend experimental tests with optical traps.

## Key findings

- Finite boson density in 1D and 2D at low temperatures
- Regularization techniques alter traditional no-go theorems
- Potential for BEC 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.