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Large-volume, high-temperature Bose-Einstein condensation is illustrated for a relativistic $O(2)$-invariant scalar field with a fixed charge using the canonical ensemble. The standard, grand canonical results are reproduced for the infinite-volume limit. Finite-volume corrections are calculated in the canonical ensemble and the results are found to differ from the finite-volume grand canonical approximation in a consistent qualitative way.
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Daniel Bedingham (2003) studied this question.
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