MATHEMATICAL PHYSICS
Many contemporary problems arising in physics are often too difficult to solve exactly by analytical means. Computer assisted studies are very useful substitutes, but they have their limitations. Applying modern mathematical methods to generate estimates and/or controlled bounds on relevant quantities, or even simply to generate new insights into old problems by the study of specialized models can sometimes provide an alternative approach.Current efforts in mathematical physics are addressed to questions in quantummechanics, functional integration, quantum field theory, signal analysis, condensed matter physics, etc. The range of applications is very broad.
One specific recent example involves the use of coherent state methods to study quantization field. As part of this study it is found that noncanonical methods are required in order to respect certain aspects of the basic physics of the problem. This emphasis as well as the methods involved sets this method apart from other current methods to study quantum gravity.
In another example, methods of mathematical physics are developed and used to explore universal features in models of disordered quantum systems as well as phase transitions in classical spin systems that can be treated exactly. Such model solutions provide useful insights into real physical systems where pertubative approaches fail due to a variety of reasons. Efforts also involve generalizing existing models in these areas to increase their domains of validity.