Foundations of quantum mechanics, quantum communication and measurement, Bell inequalities, time observables, open quantum systems.

 [1]        Ensembles on Configuration Space: Classical, Quantum and Beyond

           M.J.W. Hall and M. Reginatto   (Springer, Switzerland, 2016)

The dynamics of ensembles on configuration space is shown to be a valuable tool for unifying the formalisms of classical and quantum mechanics, for deriving and extending the latter in various ways, and for addressing the quantum measurement problem. 

A description of physical systems by means of ensembles on configuration space can be introduced at a very fundamental level: the basic building blocks are a configuration space, probabilities, and Hamiltonian equations of motion for the probabilities. The formalism can describe both classical and quantum systems, and their thermodynamics, with the main difference being the choice of ensemble Hamiltonian.

Furthermore, there is a natural way of introducing ensemble Hamiltonians that describe the evolution of hybrid systems; i.e., interacting systems that have distinct classical and quantum sectors, allowing for consistent descriptions of quantum systems interacting with classical measurement devices, and quantum matter fields interacting gravitationally with a classical spacetime.

[2]        General Relativity: an introduction to black holes, gravitational waves, and cosmology

               M.J.W. Hall   (Morgan & Claypool, USA, 2018)

This concise textbook begins with a review of special relativity and tensors and then develops the basic elements of general relativity — a beautiful theory that unifies special relativity and gravitation via geometry — with applications to the gravitational deflection of light, global positioning systems, black holes, and cosmology. The recent detection of gravitational waves by the Nobel-prize winning LIGO collaboration is described, and the book closes with another recent Nobel-prize winning discovery: our accelerating Universe.

Based on a set of 18 lectures delivered over the past five years, the book provides readers with a solid understanding of the underlying physical concepts; an ability to appreciate and in many cases derive important applications of the theory; and a grounding for those wishing to pursue their studies further. A range of questions are included at the end of each chapter, and occasional ‘asides’ make connections between general relativity and other topics.

     List of Errata (as at June 2019, with thanks to Howard Wiseman and Sandra Conor):

• Eq. (4.15): the second x^β should be x^α.
• Eq. (9.14): the final ε should be εc²
• Eq. (A.9): the first equation should read L^TGL = G.