College of Liberal Arts & Sciences

# Mathematical Physics

Mathematical physics is an interdisciplinary subject where theoretical physics and mathematics intersect. The University of Iowa has held an ongoing mathematical physics seminar for the past twenty years, in which faculty from both mathematics and physics actively participate. Topics of interest include relativistic quantum mechanics, quantum field theory, representation theory of groups and quantum groups, theory of dynamical systems, quantum computing, phase transitions, quantum chaos, lattice gauge theory and C* algebras.

Our program in Mathematical Physics is one of the few in the U.S. that is fully interdisciplinary, combining both physicists and mathematicians in a working relationship. Every semester our seminar includes talks given by distinguished visitors, including Field medallists. We also organize workshops held on campus here at Iowa, attracting speakers from around the world; we've organized two such workshops in six years. Students may work on interdisciplinary research topics involving mathematics and theoretical physics. They can obtain a PhD through the University's Applied Mathematical and Computational Sciences program, in which a physicist and a mathematician jointly supervise the dissertation. Two students have recently completed such dissertations; one teaches in a mathematics department, the other is doing economic research for a private company.

## Physics and Astronomy

*Theoretical elementary particle physics; lattice gauge theory; optical lattices.*

- Lattice field theory
- Renormalization group methods
- Composite Brout-Englert-Higgs bosons
- Decays of B-mesons (with the theory group at Fermilab)
- Gauge interactions on optical lattices
- Numerical simulations on home made clusters and at national facilities
- Quantum Field Theory methods: Feynman diagrams, strong-coupling expansion, large-N approximations
- Employment of former students: postdocs at five major universities in the U.S. and one in Ireland; senior research scientist in driving simulation project; software engineer in industry; college instructor; medical physics
- Students can be involved with the theory group at Fermilab
- Students are involved weekly in two seminars
- Students travel to summer schools and conferences

*Theoretical nuclear physics; mathematical physics.*

- Current Research: Supported by NSF and DOE Office of Science
- Relativistic few-quark and few-nucleon models of light nuclei and nucleons
- Leptonic probes of few hadron systems
- Scattering using Minkowski path integrals
- Multi-scale wavelet representations of quantum fields
- The vacuum in quantum field theory
- Euclidean formulations of relativistic quantum mechanics and quantum field theory
- Numerical methods based on wavelets

*Theoretical particle physics; string theory.*

- Topics include string theory with applications in gravitation, cosmology, superstring theories as unified theory, gauge/gravity correspondence
- Numerical techniques developed for solutions in quantum chromodynamics (QCD), string theory
- Students also: interact with students at other universities; participate in interdisciplinary work with mathematics department
- Students develop mathematical skills including analytical, numerical, and symbolic methods

## Mathematics

### Palle Jorgensen

*Wavelets, quantum theory, symmetry, algorithms*

- Particles, fields, geometry, relativity, quantum computing algorithms, spectrum
- Mathematics professor, eligible to co-advise physics theses
- Author of book on wavelets
- Students develop theoretical and computational skills

### Paul Muhly

*Operator algebras and mathematical physics*

- Mathematical underpinnings of quantum mechanics, particularly those of quantum field theory and quantum statistical mechanics
- Mathematics professor, eligible to co-advise physics theses
- Students develop skills including a wide range of analytical tools from a number of fields of mathematics