Monte Carlo Methods for Quantum Field Theory

10/1/99


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Table of Contents

Monte Carlo Methods for Quantum Field Theory

Functional Integrals and QFT

Monte Carlo methods

Monte Carlo methods

Central Limit Theorem

Central Limit Theorem

Central Limit Theorem

Central Limit Theorem

Central Limit Theorem

Central Limit Theorem

Importance Sampling

Importance Sampling

Importance Sampling

Importance Sampling

Importance Sampling

Random number generators

Markov chains

Proof of convergence of Markov chains

Proof of convergence of Markov chains

Proof of convergence of Markov chains

Markov chains

Markov chains

Markov chains

Markov chains

Autocorrelations

Autocorrelations

Autocorrelations

Continuum limits

Continuum limits

Continuum limits

Continuum limits

Markov chains

Global heatbath

Global heatbath

Local heatbath

Gaussian generators

Gaussian generators

Gaussian generators

Local heatbath

Generalised Hybrid Monte Carlo

Generalised Hybrid Monte Carlo

Generalised Hybrid Monte Carlo

MDMC

MDMC

Partial Momentum Refreshment

Generalised Hybrid Monte Carlo

Generalised Hybrid Monte Carlo

Symplectic Integrators

Symplectic Integrators

Symplectic Integrators

Symplectic Integrators

Symplectic Integrators

Symplectic Integrators

Symplectic Integrators

Symplectic Integrators

Langevin algorithm

Inexact algorithms

Inexact algorithms

Inexact algorithms

Inexact algorithms

Inexact algorithms

Inexact algorithms

Local HMC

Local HMC

Classical Mechanics on Group Manifolds

Classical Mechanics on Group Manifolds

Classical Mechanics on Group Manifolds

Classical Mechanics on Group Manifolds

Classical Mechanics on Group Manifolds

Classical Mechanics on Group Manifolds

Dynamical fermions

Grassmann algebras

Grassmann algebras

Grassmann algebras

Grassmann algebras

Dynamical fermions

Dynamical fermions

Dynamical fermions

Dynamical fermions

Dynamical fermions

Krylov solvers

Krylov solvers

Krylov solvers

Krylov solvers

Higher order integrators

Higher order integrators

Higher order integrators

Instabilities

Acceptance rates

Acceptance rates

Cost and dynamical critical exponents

Cost and dynamical critical exponents

Cost and dynamical critical exponents

Cost and dynamical critical exponents

Cost and dynamical critical exponents

Cost and dynamical critical exponents

Cost and dynamical critical exponents

Reversibility

Reversibility

Reversibility

Reversibility

Update ordering for LHMC

Update ordering for LHMC

Update ordering for LHMC

Update ordering for LHMC

Update ordering for LHMC

Update ordering for LHMC

Update ordering for LHMC

Update ordering for LHMC

Chebyshev approximation

Chebyshev approximation

Chebyshev approximation

Chebyshev approximation

Chebyshev approximation

Chebyshev approximation

Multibosons

Reweighting

Noisy methods

Noisy inexact algorithms

Noisy inexact algorithms

Kennedy–Kuti algorithm

Kennedy–Kuti algorithm

Noisy fermions

Noisy fermions

Bhanot–Kennedy algorithm

“Kentucky” algorithm

“Kentucky” algorithm

Cost of noisy algorithms

Cost of noisy algorithms

Cost of noisy algorithms

PHMC

RHMC

Ginsparg–Wilson fermions

Neuberger’s operator

Neuberger’s operator

Computing Neuberger’s operator

Computing Neuberger’s operator

Author: Tony Kennedy

Email: adk@ph.ed.ac.uk

Home Page: http://www.ph.ed.ac.uk/~adk

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