Robert Singleton

Minkowski space non-Abelian classical solutions with noninteger winding number change.

Working in a spherically symmetric ansatz in Minkowski space, we discover new solutions to the classical equations of motion of pure SU(2) gauge theory. These solutions represent spherical shells of energy, which move inward near the speed of light at early times, excite the region of space around the origin at intermediate times, and move outward at late times. The solutions change the winding number in bounded regions centered at the origin by noninteger amounts. They also produce a noninteger topological charge in these regions. We show that the previously discovered solutions of Luescher and Schechter also have these properties.

Fermion production in the background of Minkowski space classical solutions in spontaneously broken gauge theory

We investigate fermion production in the background of Minkowski space solutions to the equations of motion of SU(2) gauge theory spontaneously broken via the Higgs mechanism. First, we attempt to evaluate the topological charge {ital Q} of the solutions. We find that for solutions {ital Q} is not well defined as an integral over all space-time. Solutions can profitably be characterized by the (integer-valued) change in the Higgs winding number {Delta}{ital N}{sub {ital H}}. We show that solutions which dissipate at early and late times and which have a nonzero {Delta}{ital N}{sub {ital H}} must have at least the sphaleron energy. We show that if we couple a quantized massive chiral fermion to a classical background given by a solution, the number of fermions produced is {Delta}{ital N}{sub {ital H}}, and is not related to {ital Q}.

Spherical shells of a classical gauge field and their topological charge as a perturbative expansion.

Fermion number is not conserved in the standard model1, yet reliable techniques for calculating fermion number violating rates in high energy collisions have not been fully developed. At very low energy where the processes are best described as tunnelling events, the calculational methods make use of solutions to the Euclidean field equations — instantons. At energies comparable to but below the sphaleron barrier, Euclidean methods2 and other methods in which part of the calculation is done in Euclidean space3 have also been applied. However, at energies well above the tunnelling barrier, it may be more appropriate to work directly in Minkowski space.4, 5 To this end, E. Farhi, V. V. Khoze, R. Singleton, and I are investigating solutions to the Minkowski space classical equations of motion. In the work I sketch here,6 we study SU(2) gauge theory without the Higgs field. Working in the (spatial) spherical ansatz,7 we explore solutions which have the property that in the far past they describe freely propagating incoming shells of energy. We do this by developing a perturbative expansion in the coupling g which can be used to systematically solve the equations of motion once arbitrary initial profiles have been specified. We discuss the topological charge of these solutions, which we also develop in a power series expansion in g. We show that the topological charge is nonzero at order g 5, by doing an explicit analytic calculation of the order g 5 contribution to Q for specific initial pulses. We then describe the associated anomalous fermion production in the presence of these solutions, and speculate on the physical implications of our results.

Gauge-invariant variables for spontaneously broken SU(2) gauge theory in the spherical ansatz

We describe classical solutions to the Minkowski space equations of motion of SU(2) gauge theory coupled to a Higgs field in the spatial spherical ansatz. We show how to reduce the equations to four equations for four gauge-invariant degrees of freedom which correspond to the massive gauge bosons and the Higgs particle. The solutions typically dissipate at very early and late times. To describe the solutions at early and late times, we linearize and decouple the equations of motion, all the while working only with gauge-invariant variables. We express the change in Higgs winding of a solution in terms of gauge-invariant variables.

Numerical studies of instanton induced baryon decay

We describe an application of computational techniques to the study of instanton induced baryon decay in high energy electroweak interactions.