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So far the theory of Bose-Einstein condensates (BEC) of polar molecules wasbased on an ad hoc generalization of equations for spherical atoms. Here Iadopt a rigorous pseudo-potential approach to low-energy dipolar interactionsand derive a non-linear mean-field Schrodinger equation for aharmonically-trapped condensate. I show that, effectively, the dipolarinteractions alter molecular mass. The resulting effective mass is anisotropic:to the leading order the mass is altered only for the motion along thepolarizing field. For a typical BEC of spin-polarized magnetically-interactingalkali-metal atoms the effective atomic mass is reduced by 10% from its barevalue. For a BEC of polar molecules the mass may be reduced by a factor of a1,000.

Bose-Einstein condensates of polar molecules: anisotropic interactions = anisotropic mass