Markov Chain Monte Carlo Methods in Quantum Field Theories: A Modern Primer

Abstract

We introduce and discuss Monte Carlo methods in quantum field theories. Methods of independent Monte Carlo, such as random sampling and importance sampling, and methods of dependent Monte Carlo, such as Metropolis sampling and Hamiltonian Monte Carlo, are introduced. We review the underlying theoretical foundations of Markov chain Monte Carlo. We provide several examples of Monte Carlo simulations, including one-dimensional simple harmonic oscillator, unitary matrix model exhibiting Gross-Witten-Wadia transition and a supersymmetric model exhibiting dynamical supersymmetry breaking.

arXiv commentv3: 125 pages, 33 figures, references updated. Based on the three lectures given at the 2019 Joburg School in Theoretical Physics: Aspects of Machine Learning, Mandelstam Institute for Theoretical Physics, The University of the Witwatersrand, Johannesburg, South Africa (November 11 - 15, 2019). Published as part of Springer Briefs in Physics (2020). Author version of the manuscript

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• Probing Non-perturbative Supersymmetry Breaking through Lattice Path Integrals
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