## FACULTY RESEARCH

### Ted Allen, Associate Professor

My research interests are in the general area of theoretical particle physics and gravitation. The two most prominent themes of my current research are QCD Strings and Constrained Quantization.

**Quantum Chromodynamic Strings**

Lattice calculations show that while the color force binding together a quark and an anti-quark behaves much like the electromagnetic force on very small scales, the color flux coalesces into a string-like object when the quark separation becomes appreciable on the nuclear scale. Mechanically, such a bound system acts like two point masses connected by a cord of energy. This cord, or string, can vibrate and the system can behave in more complicated and interesting ways than, say, a hydrogen atom. A while ago my collaborators and I found a model of this string and the quarks it connects that also incorporates the spin of the quarks. I am currently working to construct the quantum mechanics of this system.

**Constrained Mechanical Systems and their Quantization**

Most fundamental theories of physics have continuous symmetries that make their description of the physics redundant; they are constrained systems. The quantum mechanics of these systems must take these symmetries into account. I am interested in constructing new tools and applying existing tools to construct the quantum mechanics of constrained systems.

Other research interests of mine are the relationship between gravity, quantum mechanics, and thermodynamics; vortex dynamics and the fractional quantum Hall effect; potential models for quark confinement; and topological mass mechanisms.

### Donald Spector, Professor

My research is multi-faceted, generally focusing particle theory and mathematical physics, with opportunities for involvement by interested students. Two current areas of my work that explore ideas relevant to quantum field theory and string theory are as follows:

**Developing a geometric characterization of shape invariance.**Shape invariance is the principle underlying quantum systems that can be solved completely. Having previously showed that shape invariance is based on a BPS structure, an algebraic phenomenon known from the study of monopoles and strings, I am now aiming to use flux quantization to provide a geometrical formulation of the BPS interpretation of shape invariance, so that we know why this BPS structure appears.**Is the Hagedorn temperature a fundamental limit?**String theory appears to have a maximum possible temperature, termed the Hagedorn temperature. My work on number theory and supersymmetry has identified a whole class of additional models that also possess a Hagedorn temperature. In these models, I am examining whether this temperature is a fundamental physical limit or an artifact of the mathematical formulation. Preliminary evidence suggests that Hagedorn temperature might be an artifact that reflects the presence of a hidden sector of particles, whose interaction with ordinary matter only becomes relevant at high energies.

Other areas in which I have an interest include analog algorithms in quantum computing, cooling schedules in simulated annealing, the bosonic decay of Q-balls, the engineering of quantum potentials to produce logarithmic spectra, the use of first-order phase transitions to model phenomena in computer science, economics, and biology, and anything to do with supersymetry.

## MORE INFORMATION

To learn more about these research projects, contact the appropriate faculty member.