Relativistic Quantum Mechanics

Recommended Prerequisites

Detailed knowledge of non-relativistic Qunatum Mechanics. Good knowledge of wriiten english.

Teaching Methods

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.

Learning Outcomes

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.

Work Placement(s)

No

Syllabus

Special relativity and Lorentz covariance.
Relativistic formalism of the electromagnetic field.
Lagrangian formulation of relativistic classical fields.
Lagrangian symmetries and conservation laws.

Klein-Gordon 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.

Head Lecturer(s)

Pedro Almeida Vieira Alberto

Assessment Methods

Assessment
Exam: 50.0%
Resolution Problems: 50.0%

Bibliography

J. D. Bjorken e S. D. Drell, Relativistic Quantum Mechanics, McGraw-Hill, 1964

W. Greiner, Relativistic Quantum Mechanics, Springer-Verlag 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.