Linear fluctuations of periodic and quasiperiodic instantons

Journal Article · Sun Oct 15 04:00:00 EDT 1989 · Physical Review (Section) D: Particles and Fields; (USA)

DOI:https://doi.org/10.1103/PhysRevD.40.2684· OSTI ID:5354400

Chakrabarti, A ^[1]

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1. Centre de Physique Theorique de l'Ecole Polytechnique, 91128 Palaiseau, CEDEX, France (FR)

The linear modes (fluctuations self-dual up to first order) of a class of periodic self-dual SU(2) gauge fields are constructed explicitly. These periodic fields have two topological indices. One is {ital P}{sub {ital T}}=(8{pi}{sup 2}){sup {minus}1}S{sub T}, {ital S}{sub {ital T}} being the action over one period {ital T}. The other is {ital q} ({lt}{ital P}{sub {ital T}}), a monopolelike winding number in {ital R}{sup 3}. The number of periodic modes turns out to be (8{ital P}{sub {ital T}}{minus}4q), where {ital q}=1 for our particular class. The solutions are obtained by constructing the periodic zero modes of spinors of unit isospin in such gauge-field backgrounds. Our results are compared to those of Jackiw and Rebbi for aperiodic instantons. This exhibits clearly the role of the second index {ital q} present in our case. Quasiperiodicity is approached as a limit of successive periodic approximations. The number of modes diverges in this limit. The possible consequences of quasiperiodicity are discussed.

• OSTI ID: 5354400
• Journal Information: Physical Review (Section) D: Particles and Fields; (USA), Journal Name: Physical Review (Section) D: Particles and Fields; (USA) Vol. 40:8; ISSN 0556-2821; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FIELD THEORIES
GAUGE INVARIANCE
INSTANTONS
INVARIANCE PRINCIPLES
ISOSPIN
LIE GROUPS
MONOPOLES
PARTICLE PROPERTIES
QUANTUM FIELD THEORY
QUASI PARTICLES
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS