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sign problem in lattice QCD

Contents

Context

Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contents

Idea

In the context of nuclear physics, by the sign problem in lattice quantum chromodynamics is is meant the issue that

but

  • in many situations, notably at finite chemical potential?, the would-be probability measure turns out not to be positive definite, and in fact typically turns out to be complex,

  • which means that various numerical evaluation methods fail.

The sign problem is one of the reasons that lattice QCD fails to be a fully satisfactory construction of non-perturbative QCD even for practical purposes. For instance, much of the phase diagram of QCD remains unknown (e.g. de Forcrand 13 CQF21), since the sign problem prevents lattice QCD computations at “almost all points” in phase space (Hsu-Reeb 08).

References

Exposition:

  • Philippe de Forcrand, The sign problem in Lattice QCD, ETH 2013 (pdf)

Detailed review:

  • Keitaro Nagata, Finite-density lattice QCD and sign problem: current status and open problems (arXiv:2108.12423)

Original articles

  • Stephen D.H. Hsu, David Reeb, On the sign problem in dense QCD, Int. J. Mod. Phys. A 25, pp. 53-67 (2010) (arXiv:0808.2987)

  • V. A. Goy, V. Bornyakov, D. Boyda, A. Molochkov, A. Nakamura, A. Nikolaev, V. Zakharov, Sign problem in finite density lattice QCD, Prog Theor Exp Phys (2017) 2017 (3): 031D01 (arXiv:1611.08093)

See also:

Last revised on August 31, 2021 at 05:49:12. See the history of this page for a list of all contributions to it.