Superfluid And Superconductivity Theory And Comparing Investigations With Their Corresponding Theories Of Quantum Mechanics

The well-known Lagrangian of current superfluid systems is not relativisticcovariant, this paper gives a general relativistic covariant Lagrangian of superfluidsystems, and naturally finds the non-relativistic Lagrangian and its all correspondingtheories after making approximations. The equation of motion obtained from the oldnon-relativistic Lagrangian density is not complete, it lost some important terms. Thenew deduced equation can be approximated to the old equations of motion, the newmomentum and energy can return to the old expressions of superfluid systems undersome conditions, and the energy and momentum from the general Lagrangian densityis accurate, no ignoring some terms. This paper deduces that the divergence ofvelocity field is zero under classic superfluid, gives two different expressions ofLagrangian, gets the same equation, and finds its solutions. Using two differentLagrangian densities, this paper obtains different forces. This paper gives bothsuperfluid theory of scalar field and comparing investigations with its correspondingtheory of quantum mechanics.Lagrangian of superfluid systems is not relativistic covariant, we can think of itas some kind of relativistic covariant Lagrangian approximation under certainconditions. We propose a Lagrangian based on this idea, equations of motion of theLagrangian more than a second-order term than the equation of motion of originalLagrangian. This shows that the equation of motion obtained from the originalLagrangian density is not completely, it automatically lost the second-order items. OurLagrangian density is well up for it, so that the equation of motion is more complete.And under additional conditions it can be approximated as the original equations ofmotion.We get different conserved currents and different momentum and energy formsfrom two different Lagrangian. But after certain conditions attached the lattermomentum and energy can return to the form of superfluidity. These furtherinstructions the Lagrangian of superfluid systems can be got by our Lagrangian. Andit can be seen under the original Lagrangian density energy and momentum is ignoredsome higher-order terms, they are approximate. The energy and momentum from ourLagrangian density is more accurate, nor ignore the higher order terms. The originalenergy-momentum is just a special case of our new energy-momentum. Consequently, using strict, complete and relativistic covariant Lagrange density,via strict derivation, this paper makes amendment for current superfluid theory. Thatis, this paper gives complete and strict motion equation, gradient energy, osmoticmomentum and Magnus force. After these calculation in this paper, one can see thatcurrent superfluid theory be not strict, which makes some approximations and losesome important terms. However, this paper shows that these terms have importantphysical significances, and should not be lost. So this paper gives a new generalLagrange density and strict computing methods, in this way, these terms are keptwhich has been lost in the old superfluid theory, thus the general superfluid theory iscomplete not as before, the appearing of these terms and the superfluid conditionshave important reference values for the research on superfluid and high temperaturesuperconductor. So the working in this paper not only has very important referencevalues for superfluid and superconductor in theory, but also has very importantguiding significances to theories and experiments about superfluid andsuperconductor.