Welcome to the website for the Masters course entitled Canonical Methods in Modern Physics taught by Dr. Sean Gryb and offered by the High Energy Physics department at Radboud University. This will be an 8 week course taught in Term 3 (Feb 1 – March 25) of the 2015 – 2016 academic year. The final grade for this 3 ec course will be determined by the outcome of a final exam. Download a PDF with the full course outline here.
- Time: 13.30 – 15.30 (block 3) on Thursdays.
- Location: HG02.802 (regular), HG03.085 (March 10).
- Exercise Classes:
- Time: 10.30 – 12.30 (block 2) on Fridays.
- Location: HG02.802 (regular), HG00.065 (Feb 19), HG03.085 (March 25).
- Review Session: There will be a review session on Monday April 4 from 13:30 – 15:30 in HG02.802.
- Exam: The exam will take place on Thursday April 7 from 13:30 – 16:30 in the Hilbert room HG03.085.
- Solutions: The exam solutions are available here. You can find a PDF of the questions here.
From coordinate independence in General Relativity to the gauge principle of the Standard Model, the most fundamental theories of physics have at their core some notion of redundancy. These important redundancies show up formally as constraints on phase space. In this course, we will give an introduction to canonical methods, which represent our best tools for dealing with and understanding these kinds of redundancies. We will first study both the conceptual and mathematical origins of the basic problem, then use a series of physically important examples — including simple mechanical systems and field theories — to illustrate the key techniques in action. This will teach us how to formally treat such system using a quantum formalism. If time permits, a selection of advanced topics are also possible including a study of the constraint structure of General Relativity.
- Course Outline
- On Space and Time: A collection of quotes and links from Leibniz, Newton and Mach on the nature of absolute time and space.
- The Dirac Algorithm: A point-by-point description of Dirac’s algorithm for the canonical analysis of gauge theories.
- Worksheet 1: Barbour–Berttoti theory and the gauge principle
- Worksheet 2: Flows on phase space and Hamilton–Jacobi Theory
- Worksheet 3: The Dirac algorithm
- Worksheet 4: More examples
- Worksheet 5: The Dirac quantization of a simple finite dimensional gauge theory.
- P. Dirac. Lectures on Quantum Mechanics. Dover, 1964.
- K. Sundermeyer. Constrained Dynamics. Springer, 1982.
- M. Henneaux and C. Teitelboim. Quantization of Gauge Systems. Princeton University Press, 1994.
- L. Faddeev and R. Jackiw. Hamiltonian Reduction of Unconstrained and Constrained Systems. PRL 60(17)-1692, 1988.