Topics in Theoretical Physics

Code:

F501

Acronym:

F501

Keywords
Classification	Keyword
OFICIAL	Physics

Instance: 2013/2014 - 1S

Active?	Yes
Responsible unit:	Department of Physics and Astronomy
Course/CS Responsible:	Master in Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:F	5	Plano de Estudos do Mestrado em Física	1	-	7,5	-
			2

Teaching language

Portuguese

Objectives

Learn the basics of the method of Green's functions (GF) in quantum physics. Understand the different types of GFs and mathematical techniques for their calculation. Get practical usage habits of GFs for calculation of observable quantities. Apply techniques of conformal  field theory  to describe critical systems (with infinite correlation length). Knowledge of basic and advanced quantum mechanics courses, quantum statistical physics and mathematical methods for functions of complex variables is necessary. Knowledge of the courses complements of statistical physics and quantum field theory will be very useful for the study of conformal field theory.

Learning outcomes and competences

Learn to calculate Green functions of various types.

Understand the application contexts of Conformal Field Theory and master the basic techniques for the calculation of the corresponding observables.

Working method

Presencial

Program

I. Green functions

1. Temporal Green function, definition

2. Interaction representation, perturbative expansion of FG

3. Wick's Theorem

4. Diagramatic techniques for temporal GF

5. Thermal Green functions, definition

6. Diagramatic techniques for thermal FG

7. Green functions out of equilibrium. Keldysh formalism.

8. Diagramatic techniques for functions of Keldysh.

9. Exercises

 

II. Conformal Field theory

1. Conformal invariance of continuous phase transitions

2. Critical exponents

3. Examples: Ising model, O(N) models and Quantum Critical Point

4. Correlation functions of primary operators

5. State-operator map

6. Operator product expansion

7. Virasoro algebra

8. Minimal models

9. Weyl anomaly and Cardy formula

Mandatory literature

Cardy John 340; Scaling and renormalization in statistical physics. ISBN: 0-.521-49959-3
Di Francesco Philippe; Conformal field theory. ISBN: 0-387-94785-X

Teaching methods and learning activities

Lectures given using multimedia techniques and blackboard. Up to 40% of total course time devoted to solution and discussion of problems.

keywords

Physical sciences > Physics > Quantum mechanics > Quantum field theory
Physical sciences > Physics > Statistical physics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	75,00
Participação presencial	0,00
Prova oral	25,00
Total:	100,00

Eligibility for exams

The students should attend to at least 75% of the lectures.

Calculation formula of final grade

The final grade is a weighted average of the final exam mark (weight 75%) and the mark from the presentation of a problem/project during the course (weight 25%).