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

TL;DR

This paper develops a relativistic covariant Lagrangian for superfluid systems, revealing new equations and symmetries, and compares the superfluid scalar field theory with quantum mechanics.

Contribution

It introduces a general relativistic Lagrangian for superfluid systems, deriving complete equations of motion and uncovering fundamental symmetries and conditions.

Findings

Derived a relativistic covariant Lagrangian for superfluid systems.

Identified conditions under which classical superfluid Lagrangian approximates the general form.

Compared superfluid scalar field theory with quantum mechanics, highlighting differences and similarities.

Abstract

The well-known Lagrangian of current superfluid systems is not relativistic covariant, this paper gives a general relativistic covariant Lagrangian of superfluid systems, and naturally finds the non-relativistic Lagrangian and its all corresponding theories after making approximations. The equation of motion obtained from the old non-relativistic Lagrangian density is not complete, it lost some important terms. The new deduced equation can be approximated to the old equations of motion, the new momentum and energy can return to the old expressions of superfluid systems under some conditions, and the energy and momentum from the general Lagrangian density is accurate, no ignoring some terms. This paper reveals that the current classical superfluid Lagrangian density is only an approximation Lagrangian density under conditions: the scalar field is inverse proportional to its complex conjugate field and the square of time derivative of scalar field logarithm approximates to zero. This paper deduces that the divergence of velocity field is zero under classic superfluid, gives two different expressions of Lagrangian, gets the same equation, 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 physics equation of the superfluid, and further discover the symmetry breaking processes and the special conditions from the general Lagrangian to the special Lagrangian. This paper gives both superfluid theory of scalar field and comparing investigations with its corresponding theory of quantum mechanics.