The analysis developed by Lüscher and Schaefer of the Hybrid Monte Carlo (HMC) algorithm is extended to include Fourier acceleration. We show for the φ 4 theory that Fourier acceleration substantially changes the structure of the theory for both the Langevin and HMC algorithms. When expanded in perturbation theory, each five-dimensional auto-correlation function of the fields φ (x i ,t i ), 1 ≤ i ≤ N, corresponding to a specific 4-dimensional Feynman graph separates into two factors: one depending on the Monte-Carlo evolution times t i and the second depending on the space-time positions x i . This separation implies that only auto-correlation times at the lattice scale appear, eliminating critical slowing down in perturbation theory.

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