Matt Visser: Research Interests
Matt Visser's Research Interests
Revised January Y2K
This is now (May 2006) somewhat out of date...
Will try to update this when (if) I ever have the
time...
Quick Summary:
I am currently engaged in several major research projects. The technical thrust of these projects can be summarized as ``field theory under unusual conditions'', and the potential applications run all the way from basic quantum physics to cosmology and quantum gravity.
- Within the context of quantum field theory I have intensively studied the notion of Casimir energy, and the relationship between one-loop beta functions and the heat kernel, with applications ranging from experimental verification of the flat-plate Casimir effect through to possible quantum contributions to the cosmological constant.
- I have considered the possibility of applying quantum field theoretic techniques to the study of sonoluminescence, both via quasi-static and dynamical calculations.
- In the interface region between quantum field theory and general relativity I have been heavily involved in trying to get a deeper understanding of the energy conditions and the extent to which they should be trusted. (Not only do one-loop quantum effects violate all the energy conditions, but even certain quite seemingly sensible looking classical systems violate all the energy conditions.) The implications are potentially disturbing.
- I have also recently been interested in certain non-quantum field theories, associated with stochastic processes, that nevertheless share deep connections with quantum physics: in particular, with my collaborators I have shown that the QFT notion of the effective potential can very usefully be carried over to quite general classes of stochastic partial differential equations. Potential applications include surface growth, turbulence, and structure formation.
- On the more classical side, I have been involved in developing and extending the acoustic analog of general relativity, wherein one observes that there is a very close formal analogy between light waves moving through a curved spacetime and sound waves moving through a moving fluid: This analogy can be used to probe many of the formal aspects of classical and quantum field theories on curved spacetimes. It also serves as a clean theoretical laboratory to separate the kinematically induced properties (due to generic spacetime curvature) from the dynamically-induced properties that specifically depend on the Einstein equations.
My book, Lorentzian Wormholes --- from Einstein to Hawking, continues to sell well. Over 2500 copies have been sold as of January Y2K. The third printing is currently being depleted.
If you have already had enough, you can escape by looking at:
Homepage
Vitae
Publications
Book
Horizon: The Time Lords
Some general interest articles
Some graphics
For more information about physics at Washington University:
To the Group Page
To the Departmental Page
For more technical details on my research:
Technical details
Future plans:
As you can see from my recent publications I am engaged in several related interlocking research projects:
- Casimir energy.
- Sonoluminescence as a QED effect.
- Energy conditions and their classical and quantum violation.
- Stochastic field theories.
- The acoustic analog for general relativity.
- Looking at the effect non-conformal non-minimal couplings have on the energy conditions of general relativity (and the possible bizarre consequences).
- Investigating the acoustic analog for general relativity with a view to possibly extracting experimentally accessible predictions.
- Canonical defects in black hole thermodynamics: essential to gaining an understanding of off-shell thermodynamics.
- Exotic Kaluza-Klein theories where our world is considered as a submanifold of higher-dimensional spacetime. (This is actually a very old topic that has recently become fashionable again. One of my earliest papers [1986] has picked up more citations in the last six months than in the preceding 14 years.)
Looking to the future, I expect to continue to work on these related issues of semi-classical quantum gravity and quantum field theory under the influence of external conditions. More specifically, I plan to attack projects such as:
-
Extending or replacing the energy conditions of general relativity.
(The number and variety of situations in which the energy conditions are now known to be violated, both classically and quantally is now so large that we really should start thinking about replacements for the energy conditions, and it is already clear that something a little more complicated than just averaging along geodesics will certainly be needed.) -
Improved versions of the singularity theorem, topological censorship
theorem, superluminal censorship theorem, and positive mass
theorem.
(Improved in the sense that one should try to find input hypotheses weaker than the normal energy conditions, and in particular, weaker than the averaged null energy condition.) -
Superfield formalism for stochastic field theories.
(The stochastic field theories obtained when a partial differential equation is driven by white noise are known to possess a ``hidden'' supersymmetry. This strongly suggests that it should be possible to construct a superfield-superspace formalism, and construct a super-Feynman expansion which should greatly simplify multi-loop computations in, for example, the KPZ model.) -
General kinematic and dynamic analysis of sub-manifold variants of
Kaluza-Klein theory.
(In particular, how much of the Randall-Sundrum scenario and related scenarios are really dependent on string theory, and how much of the phenomenology is generic and independent of any underlying string theory?)
The interplay between gravity, in the form of geometrodynamics --- the dynamics of geometry --- and quantum field theory is an aspect of modern physics that continues to provide deep and subtle problems. Attempts at a full fledged quantum theory of gravity continue to be bogged down in a morass of technical and conceptual difficulties, compounded by a total lack of experimental guidance. The conceptually simpler questions of semiclassical gravity are still the best test bed we have for trying to understand the interface between gravitational and quantum phenomena.
In summary: I have a well-defined research program in mind that addresses the response of field theories in general, and quantum field theory in particular, to external conditions; whether they be boundary conditions, or classical external fields such as Einstein gravity. This research program includes a number of interlocking projects of interest to both the particle physics community, the general relativity community, and quantum physicists generally. Potential applications run the gamut from particle physics phenomenology, to condensed matter phenomenology, to cosmology.
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Other information:
Homepage
Vitae
Publications
Book: Lorentzian Wormholes---from Einstein to Hawking
Horizon: The Time Lords
Some general interest articles
Some graphics
Exit routes:
To my personal homepage
To my standardized departmental homepage
To the Mathematics Department Page