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The well-known Lagrangian of current superfluid systems is not relativisticcovariant, this paper gives a general relativistic covariant Lagrangian ofsuperfluid systems, and naturally finds the non-relativistic Lagrangian and itsall corresponding theories after making approximations. The equation of motionobtained from the old non-relativistic Lagrangian density is not complete, itlost some important terms. The new deduced equation can be approximated to theold equations of motion, the new momentum and energy can return to the oldexpressions of superfluid systems under some conditions, and the energy andmomentum from the general Lagrangian density is accurate, no ignoring someterms. This paper reveals that the current classical superfluid Lagrangiandensity is only an approximation Lagrangian density under conditions: thescalar field is inverse proportional to its complex conjugate field and thesquare of time derivative of scalar field logarithm approximates to zero. Thispaper deduces that the divergence of velocity field is zero under classicsuperfluid, gives two different expressions of Lagrangian, gets the sameequation, and finds its solutions. Using two different Lagrangian densities,this paper obtains different forces. Therefore, this paper discovers a general,fundamental and real physics symmetry Lagrangian deducing the real physicsequation of the superfluid, and further discover the symmetry breakingprocesses and the special conditions from the general Lagrangian to the specialLagrangian. This paper gives both superfluid theory of scalar field andcomparing investigations with its corresponding theory of quantum mechanics.

Dynamic Superfluid Theory of Scalar Field and Comparing Investigations with its Corresponding Theory of Quantum Mechanics