PHY344 and PHY444: Directed Reading
The aim of the directed reading course is to run selected `do it yourself' lecture courses on material which is well established and written up in text books and review articles. The topics represent important areas of theoretical physics and related mathematics which are not covered in our lecture courses. The course is assessed by three methods: continuously by submission of summary notes, by the solution of problems, and at the end by a short report and oral presentation to other theoretical physics students and to the staff.
Group Theory is concerned with what we can deduce from the symmetries of systems. These include the discrete groups associated with the finite rotation symmetries of objects like molecules, which are central to crystallography and spectroscopy, and continuous groups, such as rotations in free space, which lead into the ideas of Lie algebras. SU(2), SU(3) and the symmetries of particle physics. Arfken and Weber, Mathematical Methods for Physicists.
Green's Functions are one of the most important mathematical tools of theoretical physics; they describe, in general terms, how the disturbance due to a source at one place propagates in space and time to another place. The actual form of the Green's function depends on the differential equation which governs the field being disturbed and the boundary conditions on that field. We will look at how the Green's function is defined, how to construct it from particular solutions of the differential equation, and what it can tell us about physics. Examples will include various differential equations (Poisson's Eq., the wave Eq.), in different numbers of dimensions. The main text will be Barton's Elements of Green's Functions and Propagation, with some dipping into other books, such as Jackson's `Classical Electrodynamics' for examples.
Quantum Mechanics and Path Integrals: Feynman formulated an alternative approach to the Schrodinger wavefunction formulation of quantum mechanics. In Feynman's formulation a probability amplitude is developed that gives the probability of a particle arriving at one spacetime location from another spacetime location. This probability amplitude is proportional to the sum of exponentials of the actions for each possible spacetime path between these two points. Since the action is the time integral of the Lagrangian, this formulation unites quantum and Lagrangian mechanics. Feynman and Hibbs, Quantum Mechanics and Path Integrals.
Quantum Information and Computation are very topical research area involving physicists in a range of traditional subjects where quantum effects are important, including semiconductors, superconductors, NMR and atomic physics, along with many mathematicians. This project will introduce the basic ideas of using quantum mechanics for efficient computation, error correction, algorithms, secure communication etc, and also cover some of the experimental progress in making these ideas a reality. Nielsen and Chuang, Quantum Computation and Quantum Information.