  The Hugenholtz-Pines (HP) theorem is derived for Bose-Einstein condensates
(BECs) with internal degrees of freedom. The low-energy Ward-Takahashi identity
is provided in the system with the linear and quadratic symmetry breaking
terms. This identity serves to organize the HP theorem for multicomponent BECs,
such as the binary BEC as well as the spin-$f$ spinor BEC in the presence of a
magnetic field with broken U$(1)$$\times$SO$(3)$ symmetry. The experimental
method based on the Stern-Gerlach experiment is proposed for studying the
Ward-Takahashi identity.
