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{{Short description|Non-Abelian gauge field used in modern field theory}}
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{{Short description|Non-Abelian gauge field used in modern field theory}}


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A '''quantum Yang-Mills field''' is a non-Abelian gauge field: a field associated with a symmetry group whose generators do not all commute. Yang-Mills fields generalize electromagnetism and are essential for the strong interaction, the weak interaction, and the structure of the Standard Model. Unlike the electromagnetic field, non-Abelian gauge fields can interact directly with themselves.<ref>{{cite web |title=Yang-Mills theory |url=https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory |website=Wikipedia |access-date=19 May 2026}}</ref><ref>{{cite book |last1=Peskin |first1=Michael E. |last2=Schroeder |first2=Daniel V. |title=An Introduction to Quantum Field Theory |publisher=Addison-Wesley |year=1995 |id=ISBN 978-0-201-50397-5}}</ref>
'''Yang-Mills field''' is a Book II topic in the Quantum Collection. A quantum Yang-Mills field is a non-Abelian gauge field: a field associated with a symmetry group whose generators do not all commute. Yang-Mills fields generalize electromagnetism and are essential for the strong interaction, the weak interaction, and the structure of the Standard Model. Unlike the electromagnetic field, non-Abelian gauge fields can interact directly with themselves. A quantum Yang-Mills field is a non-Abelian gauge field: a field associated with a symmetry group whose generators do not all commute. Yang-Mills fields generalize electromagnetism and are essential for the strong interaction, the weak interaction, and the structure of the Standard Model. Unlike the electromagnetic field, non-Abelian gauge fields can interact directly with themselves.
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Latest revision as of 22:06, 20 May 2026



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Yang-Mills field is a Book II topic in the Quantum Collection. A quantum Yang-Mills field is a non-Abelian gauge field: a field associated with a symmetry group whose generators do not all commute. Yang-Mills fields generalize electromagnetism and are essential for the strong interaction, the weak interaction, and the structure of the Standard Model. Unlike the electromagnetic field, non-Abelian gauge fields can interact directly with themselves. A quantum Yang-Mills field is a non-Abelian gauge field: a field associated with a symmetry group whose generators do not all commute. Yang-Mills fields generalize electromagnetism and are essential for the strong interaction, the weak interaction, and the structure of the Standard Model. Unlike the electromagnetic field, non-Abelian gauge fields can interact directly with themselves.

Yang-Mills field: non-Abelian gauge curvature and self-interacting field lines.

Gauge symmetry

Yang-Mills theory begins with local gauge symmetry. The gauge field is introduced so that the theory remains consistent when internal symmetry transformations vary from point to point in spacetime.[1]

Self-interaction

Because the underlying symmetry is non-Abelian, the field strength contains terms in which gauge fields multiply one another. This produces self-interactions that are absent in ordinary Abelian electromagnetism.[2]

Physical examples

Quantum chromodynamics is a Yang-Mills theory based on color SU(3), with gluon fields as its gauge fields. The electroweak theory also uses non-Abelian gauge fields before symmetry breaking separates the observed photon, W, and Z bosons.[3]

Description

Yang-Mills field is a matter-scale concept used to organize how quantum theory describes atoms, particles, fields, condensed matter, plasma, or spacetime-related systems. In the Quantum Collection it is placed by scale so the reader can move from materials and molecules down to subatomic degrees of freedom.

Quantum context

At this scale, the relevant behavior is controlled by quantized states, interactions, conservation laws, and the way excitations or particles are observed. The concept is normally linked to measurable properties such as energy, momentum, charge, spin, spectra, scattering rates, or collective modes.

Role in the collection

This page provides a compact reference point for related pages in Book II. It should be read together with nearby matter-scale topics and the corresponding foundations in quantum mechanics.[4]

See also

Table of contents (84 articles)

Index

Full contents

References

  1. ↑ Schwartz, Matthew D. (2014). Quantum Field Theory and the Standard Model. Cambridge University Press. ISBN 978-1-107-03473-0. 
  2. ↑ "Yang-Mills theory". https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory. 
  3. ↑ "Review of Particle Physics". Physical Review D 110 (3): 030001. 2024. DOI 10.1103/PhysRevD.110.030001. 
  4. ↑ "Quantum mechanics". https://en.wikipedia.org/wiki/Quantum_mechanics. 


Author: Harold Foppele


Source attribution: Physics:Quantum Yang-Mills field

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