Chiral asymmetry and the Atiyah-Patodi-Singer index for the Dirac operator on a four-dimensional ball

Journal Article · Mon Jun 15 00:00:00 EDT 1987 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.35.3995· OSTI ID:6058226

Schmidt, J R; Bincer, A M

We consider the problem of determining the zero modes for the massless Dirac operator in a background Abelian gauge field F on a four-dimensional Euclidean manifold M with a boundary partialM. We solve exactly the case when F is constant self-dual or anti-self-dual and M is B/sup 4/, a four-dimensional ball, so that partialM is S/sup 3/, a three-dimensional sphere. The analysis employs the Atiyah-Patodi-Singer index theorem for manifolds with boundaries.

• Research Organization: Physics Department, University of WisconsinMadison, Madison, Wisconsin 53706
• OSTI ID: 6058226
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 35:12; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645204* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Strong Interactions & Properties
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ASYMMETRY
CHIRALITY
DIRAC OPERATORS
EIGENVALUES
ELECTROMAGNETIC FIELDS
ELEMENTARY PARTICLES
EUCLIDEAN SPACE
FOUR-DIMENSIONAL CALCULATIONS
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
MASSLESS PARTICLES
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MULTIPLICITY
PARTICLE PROPERTIES
QUANTUM OPERATORS
RIEMANN SPACE
SPACE
SYMMETRY BREAKING