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By Radford M. Neal. Chapter 5 of Handbook of Markov Chain Monte Carlo.

Author chapter: sites.stat.columbia.edu/gelman/bayescomputation/Neal2011.pdf

Sections 5.3.1–5.3.2 define the augmented canonical density, refreshed Gaussian momenta, leapfrog-based proposal, Metropolis correction and proof of invariance. The chapter dates from 2011; its arXiv posting is later.

Radford M. Neal works on Bayesian inference, machine learning and computational methods for complex probability distributions. His research page lists neural networks, Gaussian processes and Markov chain Monte Carlo.^[ref]

His MCMC Using Hamiltonian Dynamics by Radford M. Neal develops Hamiltonian Monte Carlo: introduce auxiliary momenta, simulate approximately energy-preserving motion and correct discretization error with a Metropolis–Hastings algorithm. Longer, directed proposals can explore a target more effectively than a diffusive random walk. The combination of volume preservation, reversibility and an acceptance correction explains why an approximate numerical trajectory can still produce the intended invariant distribution.^[ref]