Effective Classical Hamiltonian from Perturbatively Defined Path   Integral
  Introducing a perturbative definition, phase space path integrals can be calculated without slicing. This leads to a short-time expansion of the quantum-mechanical path amplitude, or a high-temperature expansion of the unnormalized density matrix, respectively. We use the proposed formalism to calculate the effective classical Hamiltonian for the harmonic oscillator. 
Michael Bachmann
quant-ph cond-mat.stat-mech