"Relativistic Quantum Physics" is a course where important theories for elementary particle physics and symmetries are learned. During the course, it will be illustrated how relativistic symmetries and gauge symmetries can restrict "possible" theories. The course will give an introduction to perturbation theory and Feynman diagrams. The problem with divergencies will be mentioned and the concepts for regularization and renormalization will be illustrated.

### Choose semester and course offering

Choose semester and course offering to see information from the correct course syllabus and course offering.

## Content and learning outcomes

### Course contents

I. Relativistic quantum mechanics

Tensor notation. Casimir operators. The Poincaré group. Irreducible representations of particles. The Klein-Gordon equation. The Dirac equation. The structure of Dirac particles. The Dirac equation: central potentials. The Weyl equation. Maxwell's equations and quantization of the electromagnetic field. Introduction to Yang-Mills theory.

II. Introduction to quantum field theory

Neutral and charged Klein-Gordon fields. The Dirac field. The Majorana field. Asymptotic fields: LSZ formulation. Perturbation theory. Introduction to quantum electrodynamics. Interacting fields and Feynman diagrams. Elementary processes of quantum electrodynamics. Introduction to radiative corrections.

### Intended learning outcomes

After completion of the course you should be able to:

• apply the Poincaré group as well as classify particle representations.
• analyze the Klein-Gordon and the Dirac equations.
• solve the Weyl equation.
• know Maxwell's equations and classical Yang-Mills theory.
• quantize Klein-Gordon, Dirac, and Majorana fields as well as formulate the Lagrangian for these fields.
• use perturbation theory in simple quantum field theories.
• formulate the Lagrangian for quantum electrodynamics as well as analyze this.
• derive Feynman rules from simple quantum field theories as well as interpret Feynman diagrams.
• analyze elementary processes in quantum electrodynamics.
• compute radiative corrections to elementary processes in quantum electrodynamics.

### Course Disposition

No information inserted

## Literature and preparations

### Specific prerequisites

Recommended prerequisites:
Quantum Physics.
Relativity Theory.
Analytical Mechanics and Classical Field Theory (recommended).

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

The course literature consists of one book (mainly):

• T. Ohlsson, Relativistic Quantum Physics, Cambridge (2011)

• A.Z. Capri, Relativistic Quantum Mechanics and Introduction to Quantum Field Theory, World Scientific (2002)
• C. Doran and A. Lasenby, Geometric Algebra for Physicists, Cambridge (2003)
• W. Greiner, Relativistic Quantum Mechanics - Wave Equations, Springer (2000)
• F. Gross, Relativistic Quantum Mechanics and Field Theory, Wiley (1993)
• J. Mickelsson, T. Ohlsson, and H. Snellman, Relativity Theory, KTH (2005)
• M.E. Peskin and D.V. Schroeder, Introduction to Quantum Field Theory, Harper-Collins (1995)
• H.M. Pilkuhn, Relativistic Quantum Mechanics, Springer (2003)
• L.H. Ryder, Quantum Field Theory, 2nd ed., Cambridge (1996)
• F. Schwabl, Advanced Quantum Mechanics, Springer (1999)
• F.J. Ynduráin, Relativistic Quantum Mechanics and Introduction to Field Theory, Springer (1996)

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

A, B, C, D, E, FX, F

### Examination

• INL1 - Assignments, 4,5 hp, betygsskala: A, B, C, D, E, FX, F
• TEN1 - Examination, 3,0 hp, betygsskala: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

### Other requirements for final grade

Hand in assignments (INL1; 4,5 university credits) and an oral exam (TEN1; 3 university credits).

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

## Further information

### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SI2390

Physics

Second cycle