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We explain from first principles why satisfying conservation laws in BoseEinstein condensate dynamics requires many-body theory. For theGross-Pitaevskii mean-field we show analytically and numerically thatconservation laws are violated. We provide examples for angular momentum andlinear momentum conservation. Arbitrarily large violations occur despitenegligible depletion and interaction energy. For the case of angular momentumwe show through extensive many-body simulations how the conservation law can begradually restored on the many-body level. Implications are discussed.

Conserving symmetries in Bose-Einstein condensate dynamics requires many-body theory