I Hamiltonian formalism and partition function

[Simobartz]

TL;DR Summary

is it possible to find a (q,p) couple for a dipole in a magnetic field?

In hamiltonian formalism we have the generalized coordinates $q_i$ and the conjugates moments $p_i$.
For a dipole in a give magnetic field $B$ the Hamiltonian is $H=-\mu B cos \theta$ where $\theta$ is the angle between $\vec \mu$ and $\vec B$.
Can i consider $\theta$ or $cos \theta$ as a generalized coordinate? if yes what is the associated conjugate momentum $P_\theta$?
I ask this question because i'd like to compute the partition function for a dipole in a magnetic field starting from $\frac 1 {\hbar ^f} \int dr^fdp^f exp(-\beta H(r_1...r_f,p_1...p_f))$

 

[Orodruin]

Either $\theta$ or $\cos\theta$ could be considered as a generalised coordinate. The corresponding canonical momentum would be related to angular momentum.