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{{Short description|Quantum field theory describing the strong interaction between quarks and gluons based on SU(3) gauge symmetry}}

{{Quantum book backlink|Quantum field theory}}
'''Quantum chromodynamics''' (QCD) is the quantum field theory that describes the strong interaction between quarks and gluons, based on a non-Abelian <math>SU(3)</math> gauge symmetry.<ref name="peskin">Peskin, M. E.; Schroeder, D. V. ''An Introduction to Quantum Field Theory'' (1995).</ref> It explains how quarks are bound together to form hadrons such as protons and neutrons.

<div style="float:right; border:1px solid #ccc; padding:4px; background:#fff8dc; margin:0 0 1em 1em; width:420px;">
[[File:QCD_gluon_interaction.jpg|400px]]
<div style="font-size:90%;">Gluon-mediated interaction between quarks in quantum chromodynamics, illustrating color charge exchange</div>
</div>

== Fundamental particles ==
QCD involves two types of fundamental particles:

* '''Quarks''' – matter fields carrying color charge
* '''Gluons''' – gauge bosons mediating the strong force

Quarks come in different “colors” (analogous to charge), while gluons carry combinations of color and anticolor.<ref name="weinberg">Weinberg, S. ''The Quantum Theory of Fields'' (1995).</ref>

== Gauge symmetry ==
The symmetry group of QCD is <math>SU(3)</math>, which is non-Abelian. The generators satisfy:
<math>
[T_a, T_b] = i f_{abc} T_c
</math>

This non-commuting structure leads to self-interactions of the gauge fields (gluons).<ref name="schwartz">Schwartz, M. D. ''Quantum Field Theory and the Standard Model'' (2014).</ref>

== QCD Lagrangian ==
The QCD Lagrangian is:
<math>
\mathcal{L} = \bar{\psi}_i (i\gamma^\mu D_\mu - m)\psi_i - \frac{1}{4} F_{\mu\nu}^a F^{\mu\nu a}
</math>

where:

* <math>D_\mu = \partial_\mu + i g A_\mu^a T_a</math>
* <math>F_{\mu\nu}^a</math> is the non-Abelian field strength tensor
* <math>g</math> is the strong coupling constant

This describes both quark dynamics and gluon interactions.<ref name="peskin"/>

== Gluon self-interaction ==
Unlike photons in QED, gluons carry color charge and interact with each other.

This leads to:

* nonlinear dynamics
* complex field configurations
* strong coupling behavior at low energies

Gluon self-interactions are a defining feature of QCD.<ref name="weinberg"/>

== Confinement ==
Quarks and gluons are never observed in isolation. Instead, they are confined within composite particles called hadrons.

As quarks are separated, the force between them does not decrease but remains strong, effectively preventing their isolation.

This phenomenon is known as '''confinement''' and is a key prediction of QCD.<ref name="zee">Zee, A. ''Quantum Field Theory in a Nutshell'' (2010).</ref>

== Asymptotic freedom ==
At very high energies (short distances), the strong coupling becomes weaker. This property is known as asymptotic freedom.

It is described by the running coupling:
<math>
\alpha_s(\mu)
</math>

which decreases as the energy scale <math>\mu</math> increases.

This behavior was a major theoretical breakthrough and confirmed experimentally.<ref name="peskin"/>

== Hadrons and bound states ==
Quarks combine to form:

* '''baryons''' (three quarks, e.g., proton, neutron)
* '''mesons''' (quark–antiquark pairs)

These composite particles are the observable states of QCD.

The internal structure of hadrons is governed by the dynamics of quarks and gluons.

== Role in the Standard Model ==
QCD is one of the three fundamental interactions in the Standard Model, alongside:

* electroweak interaction
* (and gravity outside the model)

It is responsible for binding quarks into nucleons and nucleons into atomic nuclei.

== Conceptual importance ==
Quantum chromodynamics demonstrates how non-Abelian gauge symmetry leads to rich and complex physical phenomena such as confinement and asymptotic freedom.

It is a cornerstone of modern particle physics and essential for understanding the structure of matter.

==See also==
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

==References==
{{reflist|3}}
{{Author|Harold Foppele}}

{{Sourceattribution|Quantum field theory (QFT) core|1}}

Physics:Quantum chromodynamics (QCD) - Revision history

imported>WikiHarold: Repair Quantum Collection B backlink template

imported>WikiHarold: Repair Quantum Collection B backlink template