The course will be divided into three 5-week modules; for each one there are four lectures (3hrs each) and four exercise sessions (3hrs each). At the end of the module there is an exam. All exams are pass/fail. You need to pass all three exams to receive credit for the course. PhD students are not obliged to do the exams, which are meant for Master students who intend to use this course as part of their Master Program.

Please register here before the course begins. Those who are not registered will not receive their grades (or other important notices).  Also register if you do not want to take the course for credit. REGISTRATION IS CLOSED

Course summary

Lectures will take place on Mondays at 11:15 - 13:00, followed by a study/exercise session 13:45- end. The location of the modules rotate: The first module will take place in Amsterdam, the second module will take place in Leiden, and the third will take place in Utrecht. Please take note of the rooms below. 

Travel Cost Reimbursement
Students who do not have an OV-card from the Dutch government can have their travel costs reimbursed from Delta ITP.

Module 1: Spontaneous symmetry breaking in the context of Condensed Matter Physics - Jasper van Wezel (Amsterdam)

Lectures: Feb 5, 12, 19, 26


Location: Amsterdam Science Park 904, room G5.29 

EXAM: Mar 5


Abstract: In this course, we will learn to recognise the many ways in which symmetry breaking impacts physics. We will use the context of condensed matter physics to discuss the general principles of which different types of symmetry exist, which can or cannot be broken, how symmetry breaking is described and what its many implications are. We will also introduce some group theoretical methods to analyse which order parameters and conjugate fields may be expected to arise in any given theory, and how many type A or type B Nambu-Goldstone modes result from them. Finally, we will discuss the similarities and differences between symmetry and gauge freedom, and see how the Higgs mechanism and various associated effects are related to symmetry breaking. 

Module 2: TBA - 
Alexey Boyarsky (Leiden) 

Lectures: Mar 12, 19, 26, Apr 9, [Apr 2 is Easter]

Location/Room: TBA (in Leiden)

EXAM: Apr 16


Abstract: TBA

Module 3
: Spontaneous symmetry breaking and non-perturbative dynamics - Irene Valenzuela (Utrecht) 

Lectures: Apr 23, 30, May 7, 14 [May 21 is Pentecost]


Location/Room: TBA (in Utrecht)

EXAM: May 28


Abstract: Even if a symmetry is spontaneously broken in any finite order of perturbation theory in quantum field theory (QFT), it can be restored at non-perturbative level in certain cases. More concretely, the Coleman-Mermin-Wagner theorem states that a continuous global symmetry cannot be spontaneously broken at finite temperature in dimension $D\leq 2$. This is at the core of many Condensed Matter systems as well as Higher Energy physics phenomena. In this course we will study the restoration of global symmetries in quantum field theories including both scalar and gauge fields in low dimensions. To that end, we will learn the tools to account for non-perturbative effects (instantons) in QFT representing the analogous of a tunneling transition in quantum mechanics.

We will cover the following topics:


- Basics of spontaneous symmetry breaking and phase transitions in QFT.


- Instantons in Abelian systems: quantum field theory beyond the perturbative level.


- Restoration of symmetry in scalar field theories: 1D Ising model and 2D Kosterlitz–Thouless transition.


- Restoration of symmetry in gauge field theories: Abelian-Higgs model, theta-vacuum structure of gauge theories and confinement in compact QED.


- Trouble with global symmetries in quantum gravity.

Contact

Dr. Enrico Pajer (Utrecht)
e-mail: e.pajer at uu.nl

Prof. Koenraad Schalm (Leiden)
email: kschalm at lorentz.leidenuniv.nl

Dr. Wouter Waalewijn (Amsterdam) 
e-mail: w.j.waalewijn at uva.nl

Administrative matters 

Wanda Verweij
 
e-mail: w.l.verweij at uu.nl

Institute for Theoretical Physics
 | Utrecht University | 
Princetonplein 5 | 
3584 CC Utrecht|