Berry's connection for non-Abelian, chiral fermions

Journal Article · Mon Jan 15 04:00:00 EST 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.41.561· OSTI ID:6954746

Isler, K; Paranjape, M B ^[1]

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1. Laboratoire de Physique Nucleaire, Universite de Montreal, Case Postale 6128, Succursale A, Montreal, Quebec, Canada (CA)

We study the set of Hamiltonians corresponding to second-quantized chiral fermions interacting with non-Abelian background gauge fields in 1+1 dimensions. The spectral projections define a Hilbert bundle over the space of gauge-field configurations with a natural, flat, connection. The projection of this connection onto a one-dimensional, nondegenerate eigenstate defines the Berry connection. We compute this connection and calculate the first Chern number of this subbundle over noncontractible two-spheres in the group of gauge transformations.

• OSTI ID: 6954746
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 41:2; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

645300* -- High Energy Physics-- Particle Invariance Principles & Symmetries
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
CHIRAL SYMMETRY
DIFFERENTIAL EQUATIONS
EIGENSTATES
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
GAUGE INVARIANCE
HAMILTONIANS
HILBERT SPACE
INVARIANCE PRINCIPLES
LIE GROUPS
MAGNETIC MONOPOLES
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MONOPOLES
PARTIAL DIFFERENTIAL EQUATIONS
POSTULATED PARTICLES
QUANTIZATION
QUANTUM OPERATORS
SCHROEDINGER EQUATION
SPACE
SYMMETRY
SYMMETRY GROUPS
TWO-DIMENSIONAL CALCULATIONS
U GROUPS
U-1 GROUPS
WAVE EQUATIONS