Physics:Quantum spinor field: Difference between revisions
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{{Short description|Quantum field whose components transform as spinors}} | {{Short description|Quantum field whose components transform as spinors}} | ||
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A '''quantum spinor field''' is a field whose components transform as spinors under rotations and Lorentz transformations. In relativistic quantum field theory, spinor fields describe spin-1/2 matter such as electrons, quarks, neutrinos, and other fermions. Unlike scalar fields, spinor fields carry intrinsic spin structure and obey anticommutation rules that encode the Pauli exclusion principle.<ref>{{cite web |title=Spinor field |url=https://en.wikipedia.org/wiki/Spinor_field |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 | | A '''quantum spinor field''' is a field whose components transform as spinors under rotations and Lorentz transformations. In relativistic quantum field theory, spinor fields describe spin-1/2 matter such as electrons, quarks, neutrinos, and other fermions. Unlike scalar fields, spinor fields carry intrinsic spin structure and obey anticommutation rules that encode the Pauli exclusion principle.<ref>{{cite web |title=Spinor field |url=https://en.wikipedia.org/wiki/Spinor_field |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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== Fermionic quantization == | == Fermionic quantization == | ||
When quantized, spinor fields use creation and annihilation operators that anticommute rather than commute. This mathematical structure prevents identical fermions from occupying the same quantum state and is essential for the stability of matter.<ref>{{cite book |last=Schwartz |first=Matthew D. |title=Quantum Field Theory and the Standard Model |publisher=Cambridge University Press |year=2014 | | When quantized, spinor fields use creation and annihilation operators that anticommute rather than commute. This mathematical structure prevents identical fermions from occupying the same quantum state and is essential for the stability of matter.<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> | ||
== Role in the Standard Model == | == Role in the Standard Model == | ||
The matter particles of the Standard Model are represented by spinor fields coupled to gauge fields and, through mass terms or Yukawa interactions, to the Higgs field. The spinor-field viewpoint separates the particle excitation from the underlying field.<ref>{{cite journal |collaboration=Particle Data Group |title=Review of Particle Physics |journal=Physical Review D |volume=110 |issue=3 |pages=030001 |year=2024 | | The matter particles of the Standard Model are represented by spinor fields coupled to gauge fields and, through mass terms or Yukawa interactions, to the Higgs field. The spinor-field viewpoint separates the particle excitation from the underlying field.<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
A quantum spinor field is a field whose components transform as spinors under rotations and Lorentz transformations. In relativistic quantum field theory, spinor fields describe spin-1/2 matter such as electrons, quarks, neutrinos, and other fermions. Unlike scalar fields, spinor fields carry intrinsic spin structure and obey anticommutation rules that encode the Pauli exclusion principle.[1][2]
Spin and Lorentz structure
A spinor field has several components because it must represent how a fermionic state changes under spacetime transformations. Dirac, Weyl, and Majorana spinors are common forms used for different physical assumptions about mass, chirality, and particle-antiparticle relations.[3]
Fermionic quantization
When quantized, spinor fields use creation and annihilation operators that anticommute rather than commute. This mathematical structure prevents identical fermions from occupying the same quantum state and is essential for the stability of matter.[4]
Role in the Standard Model
The matter particles of the Standard Model are represented by spinor fields coupled to gauge fields and, through mass terms or Yukawa interactions, to the Higgs field. The spinor-field viewpoint separates the particle excitation from the underlying field.[5]
See also
Table of contents (84 articles)
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4. Molecules (6) Back to index
5. Nuclear matter (6) Back to index
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7. Particles (12) Back to index
8. Composite particles (12) Back to index
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10. Vacuum and spacetime (12) Back to index
References
- ↑ "Spinor field". https://en.wikipedia.org/wiki/Spinor_field.
- ↑ Peskin, Michael E.; Schroeder, Daniel V. (1995). An Introduction to Quantum Field Theory. Addison-Wesley. ISBN 978-0-201-50397-5.
- ↑ "Dirac field". https://en.wikipedia.org/wiki/Dirac_field.
- ↑ Schwartz, Matthew D. (2014). Quantum Field Theory and the Standard Model. Cambridge University Press. ISBN 978-1-107-03473-0.
- ↑ "Review of Particle Physics". Physical Review D 110 (3): 030001. 2024. DOI 10.1103/PhysRevD.110.030001.
Author: Harold Foppele
Source attribution: Physics:Quantum spinor field