Summable chains of instantons: Green's functions and the Prasad-Sommerfield limit

Journal Article · Wed Apr 15 04:00:00 EST 1981 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.23.1781· OSTI ID:6391874

Boutaleb-Joutei, H; Chakrabarti, A; Comtet, A

We construct, for each homotopy class, a type of instanton configuration which exhibits many special, simple properties. The basic reason behind such properties is indicated by deriving our configuration in the 't Hooft gauge, starting from a class of particularly simple, static, and self-dual solutions in de Sitter space. Apart from this we consider, in this paper, mostly results for flat Euclidean space. We show that the static solutions are equivalent to multiply charged instantons at the origin in Witten's sense. Green's functions for this class of instanton background are studied. The known flat-space results of Brown et al. are shown to be reducible, for our case, to totally explicit and relatively compact forms. The sums over different indices arising in their formalism are performed. The inversion of a matrix, necessary for the isospin-1 massless scalar field, is carried out explicitly, for our configuration, for arbitrary index of the background instanton field. Green's functions for the Prasad-Sommerfield case are obtained as limits of our results directly in summed-up forms. Green's functions are studied also in de Sitter space. Special features due to periodic time are pointed out.

• Research Organization: Centre de Physique Theorique de l'Ecole Polytechnique, Plateau de Palaiseau, 91128 Palaiseau, Cedex, France
• OSTI ID: 6391874
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 23:8; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645201* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- General & Scattering Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DE SITTER GROUP
ELEMENTARY PARTICLES
EUCLIDEAN SPACE
FUNCTIONS
GAUGE INVARIANCE
GREEN FUNCTION
INSTANTONS
INVARIANCE PRINCIPLES
ISOSPIN
LIE GROUPS
MASSLESS PARTICLES
MATHEMATICAL SPACE
PARTICLE PROPERTIES
QUASI PARTICLES
RIEMANN SPACE
SCALAR FIELDS
SPACE
SYMMETRY GROUPS