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January 2016 PX408: Relativistic Quantum Mechanics Tim Gershon ([email protected]) Objectives At the end of this module you should: • have an appreciation of the general nature of Relativistic Quantum Mechanics. • have an understanding of the Dirac equation, its significance and its transformation properties • be able to explain how some physical phenomena including spin, the gyromagnetic ratio of the electron and the fine structure of the hydrogen atom can be accounted for using relativistic quantum mechanics Prerequisites A thorough grounding in relativity, quantum mechanics, electromagnetism and electrodynamics is assumed. Formally, the module leads from the following modules: • PX148 Classical Mechanics & Relativity • PX262 Quantum Mechanics and its Applications Additional experience in quantum physics would be useful, for example from the following modules: • PX101 Quantum Phenomena • PX382 Quantum Physics of Atoms Basic (PX147, PX274) or more advanced (PX395, PX445) knowledge of nuclear and particle physics, as well as advanced mathematics (eg. from PX440 Mathematical Methods for Physicists III) will also be useful but are not prerequisites. Note also that the module leads to • PX430 Gauge Theories of Particle Physics and may be relevant for other final year modules on quantum theory and quantum phenomena. Books The classic text for this material is • “Quantum Electrodynamics”, Feynman (1961, reissued 1998) Note that the text uses a different notation to that which will be used in the lectures and handouts. Another classic text that could be of interest, but again with inherent challenges in the notation, is • “The Principles of Quantum Mechanics”, 4th edition, Dirac (1981). Brief introductions to relativistic quantum mechanics can be found in most of the basic particle physics text books, for example: • “Introduction to High Energy Physics”, 4th edition, Perkins (2000). • “Introduction to Elementary Particles”, 2nd edition, Griffiths (2008). • “The Ideas of Particle Physics”, 3rd edition, Coughlan, Dodd & Gripaios (2006). • “An Introduction to the Standard Model of Particle Physics”, 2nd edition, Cottingham and Greenwood (2007). More advanced texts that also cover much of the material in PX430: Gauge Theories for Particle Physics would be suitable for those intending to also take that module. • “Modern Particle Physics”, Thomson (2013) • “Gauge Theories in Particle Physics”, 4th edition (2013), Aitchison & Hey. This text comes in two volumes – all the material relevant for RQM is in volume 1. The 3rd edition (2004; two volumes) and 2nd edition (1989; one volume) also cover the RQM material, but are obviously not up-to-date on the latest particle physics results. • “Particle Physics: A Comprehensive Introduction”, Seiden (2005) • “Quantum Field Theory”, revised edition, Mandl & Shaw (1993) • “Quarks and Leptons”, Halzen & Martin (1984) Several other relevant texts are available in the library. Note that while the theory covered in this module has not changed significantly for decades there have been many important experimental discoveries in that time. Hence, older texts appear dated in places, but can still be useful.