Physics:Quantum Yang-Mills field: Difference between revisions

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


{{Quantum matter backlink|Fields}}
{{Quantum matter backlink|Fields}}
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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 |isbn=978-0-201-50397-5}}</ref>
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>
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== Gauge symmetry ==
== 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.<ref>{{cite book |last=Schwartz |first=Matthew D. |title=Quantum Field Theory and the Standard Model |publisher=Cambridge University Press |year=2014 |isbn=978-1-107-03473-0}}</ref>
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.<ref>{{cite book |last=Schwartz |first=Matthew D. |title=Quantum Field Theory and the Standard Model |publisher=Cambridge University Press |year=2014 |id=ISBN 978-1-107-03473-0}}</ref>


== Self-interaction ==
== Self-interaction ==
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== Physical examples ==
== 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.<ref>{{cite journal |collaboration=Particle Data Group |title=Review of Particle Physics |journal=Physical Review D |volume=110 |issue=3 |pages=030001 |year=2024 |doi=10.1103/PhysRevD.110.030001}}</ref>
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.<ref>{{cite journal |collaboration=Particle Data Group |title=Review of Particle Physics |journal=Physical Review D |volume=110 |issue=3 |pages=030001 |year=2024 |id=DOI 10.1103/PhysRevD.110.030001}}</ref>


=See also=
=See also=

Revision as of 21:38, 19 May 2026



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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.[1][2]

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.[3]

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.[4]

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.[5]

See also

Table of contents (84 articles)

Index

Full contents

References

  1. ↑ "Yang-Mills theory". https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory. 
  2. ↑ Peskin, Michael E.; Schroeder, Daniel V. (1995). An Introduction to Quantum Field Theory. Addison-Wesley. ISBN 978-0-201-50397-5. 
  3. ↑ Schwartz, Matthew D. (2014). Quantum Field Theory and the Standard Model. Cambridge University Press. ISBN 978-1-107-03473-0. 
  4. ↑ "Yang-Mills theory". https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory. 
  5. ↑ "Review of Particle Physics". Physical Review D 110 (3): 030001. 2024. DOI 10.1103/PhysRevD.110.030001. 


Author: Harold Foppele


Source attribution: Physics:Quantum Yang-Mills field

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