Claudio Rebbi

Department of Physics and Center for Computational Science

Boston University

June 1997

Based on research by:

G.F. Bonini, C. Rebbi Boston University

S. Habib, E. Mottola, LANL

R.Singleton, Jr. University of Washington

P.Tinyakov INR, Moscow

The states of the electroweak theory are characterized by a topological number. Processes which change topology give origin to baryon number violation.

The animations below illustrate the semiclassical description of a collision process. The flux of incoming particles is represented by the imploding wave, the outgoing particles by the exploding wave. The phase of the complex field is color coded. A rainbow pattern indicates that the phase winds around the unit circle and that the state has non-trivial topology.

#### Video Sequences

Sequence 1: Collision with an energy barely above the sphaleron barrier (E_sph) which separates states of different topology. The topology changes.

Sequence 2: Collision with energy larger than **E_sph** . No change of topology.

Sequence 3: Collision with **E > E_sph**. Topology change and reduced incoming particle number.

Sequence 4: Collision with energy below the sphaleron barrier. No change of topology.

Sequence 5: Collision with **E < E_sph** . The evolution is continued along the imaginary time axis. Change of topology occurs through tunneling.

**Hardware:** SGI Power Challenge Array and SGI Origin2000.

**Software:** Fortran 77, MPI. Visualization done using IRIS Performer.

**Graphics programming assistance and video production:** Erik Brisson and Kathleen Curry, Scientific Computing and Visualization Group, Boston University.

**Acknowledgments:** Research supported by the U.S. Department of Energy