There exists a vast literature on superfluidity. It is growing daily, now that we are drawn more and more to low-dimensional systems, both theoretically and experimentally. One thing is clear: superfluidity and Bose-Einstein condensation are two distinct phenomena, the one not necessarly implying the other. I sympathize with beginners in the field; there is so much confusion, although the phenomenon is now a few years older than a century!
I would like to mention that there are some misconceptions about the validity of the well-know formulae that "define" the superfluid density as the response of the free-energy to a boundary phase-twist, or as the fluctuations of the winding number.
I attach my paper that clarifies this, Phys. Rev. B 90, 134503 (2014).
Article Superfluid density in continuous and discrete spaces: Avoidi...
It depends what you mean by superfluidity theory. If you mean the reason for which the superfluid can move without any viscosity then I develop a kinetic theory that explains this phenomenon. It extends the Boltzmann equation to the case of a dilute Bose condensed gas and tell why there is no friction. See P. Navez, Physica A 356, 241 (2005). I have more references if you wish. Let me tell also that even in this simplest case, a lot of questions remain unanswered. That makes the field still open. Contact me if you want to know more.
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