Bjorken-Johnson-Low analysis of commutator anomalies, current-divergence anomalies, and Fujikawa's relation in chiral gauge theories

Seo, K

doi:10.1103/PhysRevD.42.2819

Title: Bjorken-Johnson-Low analysis of commutator anomalies, current-divergence anomalies, and Fujikawa's relation in chiral gauge theories

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Abstract

Fermion one-loop corrections to the commutators of the gauge field, the electric field, and the charge density with the total Hamiltonian are evaluated by the Bjorken-Johnson-Low method in chiral gauge theories. It turns out that individual terms of the Hamiltonian give anomalous terms to the commutator with the electric field, but the total Hamiltonian does not. That is, the classical equation of motion for the electric field holds as the Heisenberg equation. The current-divergence anomaly is identified with the anomalous terms of the commutator between the charge density and the total Hamiltonian. These two results are combined to show that the time derivative of the Gauss-law operator amounts to the current-divergence anomaly (Fujikawa's relation).

Authors:

Seo, K ^[1]

Physics Department, Gifu City Women's College, Gifu 502 (Japan)

Publication Date:: Mon Oct 15 00:00:00 EDT 1990

OSTI Identifier:: 6227925

Resource Type:: Journal Article

Journal Name:: Physical Review, D (Particles Fields); (USA)

Additional Journal Information:: Journal Volume: 42:8; Journal ID: ISSN 0556-2821

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; FIELD THEORIES; COMMUTATORS; GAUGE INVARIANCE; CHARGE DENSITY; CHIRALITY; CLASSICAL MECHANICS; ELECTRIC FIELDS; EQUATIONS OF MOTION; FERMIONS; HAMILTONIANS; DIFFERENTIAL EQUATIONS; EQUATIONS; INVARIANCE PRINCIPLES; MATHEMATICAL OPERATORS; MECHANICS; PARTIAL DIFFERENTIAL EQUATIONS; PARTICLE PROPERTIES; QUANTUM OPERATORS; 645300* - High Energy Physics- Particle Invariance Principles & Symmetries; 645400 - High Energy Physics- Field Theory

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                    Seo, K. Bjorken-Johnson-Low analysis of commutator anomalies, current-divergence anomalies, and Fujikawa's relation in chiral gauge theories.  United States: N. p., 1990. 
        Web.  doi:10.1103/PhysRevD.42.2819.

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                    Seo, K. Bjorken-Johnson-Low analysis of commutator anomalies, current-divergence anomalies, and Fujikawa's relation in chiral gauge theories.  United States.  https://doi.org/10.1103/PhysRevD.42.2819

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                    Seo, K. 1990.  
        "Bjorken-Johnson-Low analysis of commutator anomalies, current-divergence anomalies, and Fujikawa's relation in chiral gauge theories".  United States.  https://doi.org/10.1103/PhysRevD.42.2819.

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@article{osti_6227925,

  title        = {Bjorken-Johnson-Low analysis of commutator anomalies, current-divergence anomalies, and Fujikawa's relation in chiral gauge theories},

  author       = {Seo, K},

  abstractNote = {Fermion one-loop corrections to the commutators of the gauge field, the electric field, and the charge density with the total Hamiltonian are evaluated by the Bjorken-Johnson-Low method in chiral gauge theories. It turns out that individual terms of the Hamiltonian give anomalous terms to the commutator with the electric field, but the total Hamiltonian does not. That is, the classical equation of motion for the electric field holds as the Heisenberg equation. The current-divergence anomaly is identified with the anomalous terms of the commutator between the charge density and the total Hamiltonian. These two results are combined to show that the time derivative of the Gauss-law operator amounts to the current-divergence anomaly (Fujikawa's relation).},

  doi          = {10.1103/PhysRevD.42.2819},

  url          = {https://www.osti.gov/biblio/6227925},
  journal      = {Physical Review, D (Particles Fields); (USA)},

  issn         = {0556-2821},

  number       = ,

  volume       = 42:8,

  place        = {United States},

  year         = {Mon Oct 15 00:00:00 EDT 1990},

  month        = {Mon Oct 15 00:00:00 EDT 1990}

}

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https://doi.org/10.1103/PhysRevD.42.2819

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