From Conformal Field Theory to Quantum Mechanics and Quantum Information

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***I propose to perform research in two important topics in theoretical physics: conformal field theory (CFT) and quantum mechanics (QM). My objective in both areas is to improve theoretical understanding, thereby paving the way to physical applications, both known and new.****CFT is a rich and deep subject, with many physical applications. CFTs describe systems at criticality, the world sheets of strings, quantum impurity problems, and are non-perturbatively solvable models for other physical quantum field theories. ****Much progress in understanding CFT, including many of my contributions, has come from the study of Wess-Zumino-Witten (WZW) models and related systems. Maintaining that approach, I aim to study the WZW models at fractional level, as prototypes of logarithmic CFTs; and investigate the phase model realizations of WZW fusion. ****QM is fundamental in physics. My approach is to study simple systems, from non-standard points of view, to extract new insights that apply more generally. ****Phase-space QM is one (relatively) uncommon point of view that I study, and intend to continue to examine. In addition, I aim to generalize my past work on the renormalization-group analysis of contact interactions, as well as investigate QM in a discretized alcove.****In addition to continuing my research programs in CFT and QM, I plan to shift emphasis from CFT to QM, by initiating a new line of investigation in the theory of quantum information (QI). Due to its connection with quantum computation, and the light it has shone on the fundamentals of QM, QI is currently a very exciting theme. ***My background in CFT gives me a point of view that is rare in QI, and techniques that should prove useful. For example, the quantum marginal problem is crucial in QI, since its goal is to understand the possible states of a subsystem of a composite system. In this area many of the tools I have exploited in CFT have played important roles. ***In the short term, I am studying the QI uses of complex orthogonal designs, and in the longer term, I plan to investigate the relation between quantum marginality and the open dynamics of reduced systems. ****My proposal describes a strategic mix of reliable sources of fruitful research, and new, exciting work.   It creates the opportunity for significant training of highly-qualified personnel at all levels and facilitates collaboration in Alberta (there are strong groups in Edmonton and Calgary with interests in CFT and QI, respectively), Canada, and beyond.*** *** **