Interpretation of Yang–Mills instantons in terms of locally conformal geometry

Abstract

BPST instanton and multi-instanton solutions to Yang–Mills equations are studied in the spin–charge separation formalism and in the related conformal gravity formalism. In the former instantons give non-trivial solutions to a gauged Grassmannian model, in the latter the instanton solution describes a locally conformally flat doubly wrapped cigar manifold or a more complicated manifold for multi-instanton solutions.

On spacetime rotation invariance, spin-charge separation andSU(2) Yang–Mills theory

“…The space of two-dimensional linear subspaces of R 4 is the real Grassmannian manifold Gr(4, 2) [4]. It can be described by the antisymmetric tensor [1,5,6]…”

On Lorentz Invariance, Spin-Charge Separation And SU(2) Yang-Mills Theory

“…The off-diagonal components (1) determine the embedding of a two dimensional plane in R 4 . The space of two dimensional linear subspaces of R 4 is the real Grassmannian manifold Gr(4, 2) [4], it can be described by the antisymmetric tensor [1], [5], [6]…”