Symmetries in the nuclear many-body problem: Conquering the computational scale explosion
Cottrell Scholar honoree Mark Caprio has formulated a research plan using what's called "the symplectic algebra" to understand what goes on inside the nucleus of an atom. "Symplectic" refers to a type of transformation of the spatial properties of an object. Transformations, in geometry, are specific ways in which an object can be manipulated, such as by rotating it, or continuously deforming it. "Mathematically, symplectic transformations are a generalization of SU(3) transformations," Caprio says. The term "SU(3)" refers to transformations which interchange three different types of objects. SU(3) transformations pretty much define the field of quantum chromodynamics, which deals with the interchange of various "colors" of quarks, thought to be the fundamental particles making up all matter. "Symplectic transformations change the coordinates and momenta of each particle at the same time, in a way that preserves certain relations (or symmetries) among them," Caprio says. "Symmetry," in mathematics (very loosely) covers the features of a physical system that remain unchanged under certain transformations. "Rotational symmetry," Caprio says, "is a symmetry in three-dimensional space - rotating a sphere transforms the three coordinates of every point but preserves the radius of the sphere." He adds that symplectic symmetry extends this idea to a six-dimensional space, where each point is seen as having three ordinary coordinates and three momentum components. In his theoretical research, Caprio will use the symmetries and mathematics inherent in symplectic transformations to attempt to simplify the highly complex data scientists have gathered about what goes on in the atomic nucleus. "The problem is complex because of the large number of ways protons and neutrons - also known collectively as nucleons - are able to interact," he says. By using this approach as a means to construct various computer models, Caprio is predicting he will be able to better approach the "many-body" problem inherent in the nucleus. "Many-body" refers generally to the large number of particles in the nuclei of atoms and the many ways they can interact. For example, particles at this level can also behave as waves, which is another way of saying - to a theoretical physicist, anyway—that they are carrying large amounts of information. He'll have to do some very intensive computer work to come up with an accurate, smoothly functioning model of the nucleus.
As part of his Cottrell Scholar Award, Caprio is creating a sophomore computational physics laboratory course at Notre Dame. He'll also develop computational modules for upper-level physics courses. Caprio says his goal is to "ensure that all Notre Dame physics majors acquire solid scientific computations skills over the course of their studies. Also, these enhancements will prepare students for computation in undergraduate research and integrate cutting-edge research topics into the classroom."