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theory (physics), model (physics)

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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





  • B. L. Ioffe , V. S. Fadin, L. N. Lipatov, Quantum Chromodynamics – Perturbative and Nonperturbative Aspects, Cambridge University Press (2010) (doi:10.1017/CBO9780511711817)

with emphasis on phenomenology:

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

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:


Lattice QCD checks

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)

Last revised on April 13, 2020 at 20:56:33. See the history of this page for a list of all contributions to it.