Abstract
This paper presents an advanced Physics of superfluidity and superconductivity. We know from Quantum Mechanics that there are two types of particles, bosons and fermions. Single states can be occupied by any number of bosons while for fermions a single state can be occupied at most by one fermion. The charged boson system is found to exhibit superfluidity: the gauge-invariant Lagrangian, coupling between the bosons and the electromagnetic gauge field. It is observed that current conservation puts constraints on current correlation. Current correlation functions and electromagnetic responses are then determined for superfluids and metals. The response function in a metallic conductor is used in obtaining its several parameters which include conductivity, dielectric constant, polarization, magnetic moment density and magnetic susceptibility. The London equation is then deduced for superconductors.
Highlights
Superfluidity was discovered some time after superconductivity
We have derived gauge-invariant Lagrangian for a superfluid which demonstrates the coupling between the charged superfluid particles and the electromagnetic gauge field
It shows that there is a conserved current in the superfluid field
Summary
Superfluidity was discovered some time after superconductivity. The similarity of the two words is no coincidence. A superconductor can be said to break a local symmetry spontaneously, while a superfluid breaks a global symmetry spontaneously This statement shows the theoretical similarity of the two phenomena, and emphasizes their only fundamental difference a superconducting metal is different from superfluid helium in many aspects. A charged boson system is a superfluid in which exists coupling between the bosons and the electromagnetic gauge field as well as the existence of a conserved current. The gauge – invariant Lagrangian will be derived in Section 2 to demonstrate the coupling between current or charge carriers and the electromagnetic gauge field in superfluids.
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