Quantum theory is an extraordinarily successful physical theory. Yet, over eighty years since its creation, the physical origin of key aspects of its mathematical structure remains obscure. For example, why does the quantum formalism use complex numbers and not some other number system? Why are continuous transformations represented by unitary transformations rather than some other group of transformations?

In the case of the classical theories of physics, we can trace a clear pathway from physical ideas (expressed in natural language) to physical principles (expressed in a mathematical framework), and thence to the mathematical structure of the theory itself. In the case of quantum theory, this conceptual underpinning is lacking.

In recent years, there has been great interest in creating a pathway from physical ideas to the mathematics of quantum theory—in short, in reconstructing quantum theory. One reason for this is simply the growing confidence that, after many years of a prevailing belief that understanding such a counter-intuitive theory in this way had to be intrisically beyond us, such a reconstruction might indeed be possible. Another reason is the growing belief in several quarters that such a reconstruction could contribute significantly to the development of new physical theories (such as quantum gravity).

My primary research goal over the last several years has been to develop a compelling reconstruction of quantum theory, and to investigate the insights that it provides.