Spherical Shells of Classical Gauge Field and their Topological Charge as a Perturbative Expansion

Details Spherical Shells of Classical Gauge Field and their Topological Charge as a Perturbative Expansion Spherical Shells of Classical Gauge Field and their Topological Charge as a Perturbative Expansion

1994-03-14

arxiv.org/abs/hep-ph/9403285v2

Phys.Rev.D50:4162-4174,1994

Physics

High Energy Physics

High Energy Physics - Phenomenology

18 pages in REVTEX

Scientific paper

10.1103/PhysRevD.50.4162

We consider the classical equations of motion of $SU(2)$ gauge theory, without a Higgs field, in Minkowski space. We work in the spherical ansatz and develop a perturbative expansion in the coupling constant $g$ for solutions which in the far past look like freely propagating spherical shells. The topological charge $Q$ of these solutions is typically non-integer. We then show that $Q$ can be expressed as a power series expansion in $g$ which can be nonzero at finite order. We give an explicit analytic calculation of the order $g^5$ contribution to $Q$ for specific initial pulses. We discuss the relation between our findings and anomalous fermion number violation, and speculate on the physical implications of our results.

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