
Relativistic Quantum Mechanics
F 2019 . 2020  1º semestre
Specification sheet Specific details
^{*)} N.B. if there are students who do not speak Portuguese the language is English.
Learning goals
Objectives:
Recognize the importance of Lorentz covariance. Know and be aple to apply the relativistic equations that describe the behaviour of elementar particles of spin 0 and spin 1/2 and the main consequences of extending the Principle of Relativity to quantum physics. Competences: Develop analysis and synthesis abilities; Problem solving; Critical reasoning; Capacity for autonomous learning; Research abilities. Adaptability to new situations; Criativity Syllabus
Special relativity and Lorentz covariance
Relativistic formalism of the electromagnetic field. Lagrangian formulation of relativistic classical fields. Lagrangian symmetries and conservation laws. KleinGordon equation. Free particle solutions and conserved current. Dirac equation. Spinor structure, properties of the free particle solutions. Lorentz group and its generators in spinor space. Hole theory and C, P and T symmetries of the Dirac equation. Applications to spin 0 and spin 1/2 relativistic quantum systems, including central potentials Propagators. Prerequisites
Detailed knowledge of nonrelativistic Qunatum Mechanics. Good knowledge of wriiten english.
Generic skills to reach
. Competence in analysis and synthesis;. Competence to solve problems; . Critical thinking; . Competence in autonomous learning; . Research skills; . Competence in organization and planning; . Competence in oral and written communication; . Competence in information management; . Adaptability to new situations; . Creativity; (by decreasing order of importance) Teaching hours per semester
Assessment
Bibliography of reference
J. D. Bjorken e S. D. Drell, Relativistic Quantum Mechanics, McGrawHill, 1964
W. Greiner, Relativistic Quantum Mechanics, SpringerVerlag 1994 I. J. R. Aitchison, Relativisitic Quantum Mechanics, I.J.R. Aitchison and A.J.H. Hey, Gauge Theories in Particle Physics: From Relativistic Quantum Mechanics to QED (vol 1),IOP, 2002 Teaching method
Teaching is based on the expositive method with constant references to physics systems to which the concepts learned are applied to. There is also a particular emphasis on learning the mathematical techniques needed to derive the properties and relantionships between the several quantities associated to the equations and their solutions of Relativistic Quantum Mechanics. When appropriate, students are also interrogated regarding concepts exposed or the derivation of mathematical relations, such that they can reach the correct conclusions by themselves.
Resources used
