Derivation of Aharonov Bohm effect for Quasiparticles

I've noticed the following:

Observation: Central results in the condensed matter physics rely on Aharonov Bohm-type arguments involving quasiparticles with fractional charge.

However, I can't see how these arguments are rigorous. In order for them to work, we would need a partition function of the form

$$Z[x,A]=\int Dx\,\, e^{\frac{i}{\hbar}S[x,A]},~~~~~~S[x,A]=\int_C(qA+\text{terms without A})$$

There are two issues with demonstrating the above: for one, this is describing a quantum-mechanical system, whereas quasiparticles are naturally mentioned in a field-theoretic context. So we'd need to find a way to reduce a field-theoretic partition function to a particle-partition function:

$$Z[\Psi,A]=\int D\Psi\,\, e^{\frac{i}{\hbar}S[\Psi,A]},~~~\to~~~Z[x,A]=\int Dx\,\, e^{\frac{i}{\hbar}S[x,A]}$$

The second issue would lie in finding the field-theoretic Lagrangian for a quasiparticle, but it seems like that is already known (i.e., for the fractionally charged anyons of the FQHE, just write down the Chern-Simons lagrangian). However, the first step is missing, and in a glaring way.

Last Thing:

An even better alternative, if possible, would be to derive everything in the Hamiltonian picture, taking advantage of the adiabatic theorem. The Hamiltonian for the quasiparticles would then take the form $$H=\sum_q E_q \gamma^\dagger_q \gamma_q$$

Does anyone else find it awfully surprising that no one has tried to prove the Aharonov Bohm effect in this context?

The reason that people do not go for such a "second quantized" description is that these $\gamma_q$ operators must be necessarily highly non-local for fractionalized quasiparticles. And there is typically no controlled way to "derive" such a second-quantized Hamiltonian since the system is usually strongly interacting. However, it does not mean that the fractional braiding phase has not been derived using adiabatic theorem. In fact, it was first shown in this way. Take $\nu=1/m$ Laughlin state as an example. First, following Laughlin, we have the (first-quantized) wavefunction for quasiholes, as a function of the complex coordinate of the quasihole. This was proposed by Laughlin. Then one can simply go and calculate the braiding phase of the quasiholes, as an adiabatic Berry phase. Under certain assumption about the plasma screening which has to be checked numerically, one can establish the AB phase as well as the braiding statisitcs. The original derivation was done in http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.53.722.