Relativistic quantum mechanics and introduction to quantum field theory

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Faculty: Adel Bilal
Tutors: Guilhem Semerjian, Fedor Levkovich-Maslyuk and Achilleas Passias
ECTS credits: 6
Language of instruction: English
Keywords: relativistic quantum mechanics, Dirac equation, free quantum fields, Feynman diagrams
Exam: written (3 to 4 hours)
Prerequisites: A good knowledge of (non-relativistic) quantum mechanics and some notions of special relativity. Some elementary notions of groups and their representations are useful but nor necessary. See here PDF

Description

This lecture deals with the issue of providing a relativistic framework for quantum mechanics.

After recalling the basic notions of special relativity and of quantum mechanics, the first part of the lecture deals with what is usually called “relativistic quantum mechanics”, introducing relativistic generalizations of the Schrödinger equation, namely the Klein-Gordon and Dirac equations. We study the properties and problems of these relativistic wave-equations in some detail. As a successful application we compute the relativistic spectrum of the hydrogen atom.

The second part of the lecture sets the proper framework for doing quantum mechanics in a relativistic setting by giving an introduction to quantum field theory. We will study scalar (Klein-Gordon) fields, spinor (Dirac) fields, as well as vector fields. A central point will be how to describe interactions, which will lead us to the notion of S-matrix and to the introduction (and computation!) of Feynman diagrams.

Solution of the homework

Exam of the year 2017-2018

Attached documents

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