nLab QCD


under construction



physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics

Quantum Field Theory

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



field theory:

Lagrangian field theory


quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization



States and observables

Operator algebra

Local QFT

Perturbative QFT



Quantum chromodynamics (“QCD”) is the quantum field theory of Yang-Mills theory: it describes the quantum theory of gluons and quarks.

The corresponding effective field theory that describes confined bound states such as protons is quantum hadrodynamics.



See at confinement.

Asymptotic freedom

See at asymptotic freedom.

Trace anomaly

See at QCD trace anomaly.

Phase diagram

QCD has an intricate phase diagram (e.g. Shuryak 96 Hands 01, Schaefer 05), phases including



Introduction and review:


with emphasis on phenomenology:

On QCD’s running coupling constant:

Rigorous construction as a perturbative quantum field theory via causal perturbation theory is discussed in

Survey with emphasis on non-perturbative effects:

Discussion of on-shell methods in QCD perturbation theory includes

See also

  • Bo-Lun Du, Xing-Gang Wu, Jian-Ming Shen, Stanley J. Brodsky, Extending the Predictive Power of Perturbative QCD (arXiv:1807.11144)

  • Christian Drischler, Wick Haxton, Kenneth McElvain, Emanuele Mereghetti, Amy Nicholson, Pavlos Vranas, André Walker-Loud, Towards grounding nuclear physics in QCD (arxiv:1910.07961)

As thermal field theory:

  • Jacopo Ghiglieri, Aleksi Kurkela, Michael Strickland, Aleksi Vuorinen, Perturbative Thermal QCD: Formalism and Applications (arXiv:2002.10188)

Phase diagram

On the phase diagram of QCD:

Via lattice QCD:

  • Jana N. Guenther, Overview of the QCD phase diagram – Recent progress from the lattice (arXiv:2010.15503)


On the early history of the development of quantum chromodynamics (the quark-model):

Lattice QCD

Due to confinement, the fundamental degrees of freedom in terms of which QCD is formulated, namely the quarks, are actually not the low-energy bound states of the theory, which instead are the hadrons. This leaves room to speculate that QCD is not really the fundamental theory of the strong nuclear force.

However, brute-force computation in lattice QCD shows that the quark-model does reproduce these hadron bound states somehow (even if the real understanding of how it does so remains open, this is the mass gap problem):

  • S. Durr, Z. Fodor, J. Frison, C. Hoelbling, R. Hoffmann, S.D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, K.K. Szabo, G. Vulvert,

    Ab-initio Determination of Light Hadron Masses,

    Science 322:1224-1227,2008 (arXiv:0906.3599)

    conclusion on p. 4:

our study strongly suggests that QCD is the theory of the strong interaction, at low energies as well

  • Zoltan Fodor, Christian Hoelbling, Light Hadron Masses from Lattice QCD, Rev. Mod. Phys. 84, 449, (arXiv:1203.4789)

  • S. Aoki et. al. Review of lattice results concerning low-energy particle physics (arXiv:1607.00299)

On string diagram-calculus (Cvitanović 2008: “bird tracks”) for the representation theory involved in quantum chromodynamics

Light-cone quantization

Non-perturbative QCD and hadron bound states by light-cone quantization (see there for more):

Last revised on July 4, 2023 at 10:27:00. See the history of this page for a list of all contributions to it.