Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Dirac operators coupled to vector potentials.

M F Atiyah1, I M Singer

  • 1Mathematical Institute, University of Oxford, Oxford, England.

Proceedings of the National Academy of Sciences of the United States of America
|April 1, 1984
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Through the glass lightly.

Science (New York, N.Y.)·1995
Same author

Geometry and analysis of Shimizu L-functions.

Proceedings of the National Academy of Sciences of the United States of America·1982
Same author

The peer review question.

Science (New York, N.Y.)·1981
Same author

Deformations of instantons.

Proceedings of the National Academy of Sciences of the United States of America·1977
Same author

Some Remarks on Representations of Connected Groups.

Proceedings of the National Academy of Sciences of the United States of America·1952
Same author

Plasma and blood infusion following myocardial infarction.

American heart journal·1949
Same journal

Tau protein as a regulator of mitochondrial function and dynamics.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

A scalable, dividing cell model for the robust propagation and quantification of human sporadic Creutzfeldt-Jakob disease prions.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Epigenetic regulation of mesenchymal BMP signaling directs postnatal organ innervation.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Single-shot wide-field biochemical imaging at 1 kHz frame rate.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Morphogenesis and topological evolution of a frustrated nematic liquid crystal under confinement.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

B cell-intrinsic CXCR3 drives efficient generation of ectopic pulmonary germinal center responses to influenza A virus infection.

Proceedings of the National Academy of Sciences of the United States of America·2026
See all related articles

Characteristic classes for the Dirac family index were computed using differential forms. These classes reveal obstructions to a covariant Dirac propagator, with the first obstruction linked to a chiral anomaly.

Area of Science:

  • Theoretical physics
  • Differential geometry
  • Quantum field theory

Background:

  • The Dirac equation is fundamental in relativistic quantum mechanics.
  • Gauge transformations are crucial for describing fundamental forces.
  • Covariant propagators are essential for calculating particle interactions.

Purpose of the Study:

  • To compute characteristic classes for the index of the Dirac family.
  • To identify obstructions to the existence of a covariant Dirac propagator.
  • To investigate the relationship between these obstructions and chiral anomalies.

Main Methods:

  • Utilizing differential forms on the orbit space of vector potentials.
  • Applying concepts from algebraic topology and differential geometry.

Related Experiment Videos

  • Analyzing the structure of gauge transformations.

    • Main Results:

    • Characteristic classes for the Dirac family index were successfully computed.
    • These classes were shown to represent obstructions to a covariant Dirac propagator.
    • The first obstruction was identified as being related to a chiral anomaly.

    Conclusions:

    • The study provides a new method for understanding obstructions in quantum field theory.
    • The findings offer insights into the nature of chiral anomalies.
    • This work contributes to the mathematical framework of quantum field theory and particle physics.