Quantum Field Theory
Combining special relativity with quantum mechanics led to the discovery of quantum field theory, which is needed to describe matter and its interactions at the most fundamental level. In this course you will learn how particles are field quanta and how the electromagnetic, weak and strong forces arise from symmetries and symmetry breaking.
In this course, you will learn that all matter and its interactions can be described in terms of quantum fields. In particular you learn about the theories of quantum electrodynamics, chromodynamics (strong interactions) and the electroweak theory. You will also learn how to calculate scattering amplitudes and cross sections.
The course begins with an introduction to the classical theory of fields in the Lagrangian and Hamiltonian formulations, and explores the fundamental relation between symmetries and conservation laws, as encoded in Noether's theorem. The quantum theory of fields is then developed, first, for non-interacting scalar fields, the Maxwell field and the Dirac field, clarifying the connection between quantum fields and elementary particles like photons and electrons. Then, to deal with interacting fields, the concepts of S-matrix expansion, scattering amplitudes and cross-sections, Feynman diagrams and rules, etc, are introduced and developed. Local gauge symmetry is introduced as the origin of all known interactions in nature. This directly leads to the theories of the electromagnetic force (quantum electrodynamics) and the strong nuclear force (quantum chromodynamics). To extend it to the weak force, we introduce spontaneous symmetry breaking and the Higgs mechanism as well as Yukawa couplings, and then formulate the unified
electroweak theory as an SU(2)xU(1) gauge theory. Finally, we introduce path integrals (or functional integrals) as an alternative formulation of quantum field theory.
Quantum field theory is used in many branches of physics. Hence, the course is recommended for master students who plan to pursue their studies in any branch of theoretical physics as well as students who plan to study experimental particles physics. The course is also recommended for PhD students in these areas who have not taken an equivalent course in their earlier studies.
Information for admitted students autumn 2024
Congratulations! You have been admitted at Stockholm University and we hope that you will enjoy your studies with us.
In order to ensure that your studies begin as smoothly as possible we have compiled a short checklist for the beginning of the semester.
Follow the instructions on whether you have to reply to your offer or not.
universityadmissions.se
Checklist for admitted students
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Activate your university account
The first step in being able to register and gain access to all the university's IT services.
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Register at your department
Registration can be done in different ways. Read the instructions from your department below.
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Read all the information on this page
Here you will find what you need to know before your course or programme starts.
IMPORTANT
Your seat may be withdrawn if you do not register according to the instructions provided by your department.
Information from the department
Everyone admitted to a course in Physics will receive a welcome letter with important information from us via e-mail. If you have not receive an e-mail by mid-August, please contact our Academic advisor! Unfold and read more.
Roll-call
Courses at the Department of Physics do not have a roll-call. Instead the course starts with the first lecture.
Registration
After being admitted to a course, you must register to confirm that you are starting your studies. For most of our courses this can be done online using your university account. Registration normally opens two weeks before the course starts and you must have registered at the latest one week after. If you have any problems with registration, contact our Student office. Contact details can be found below.
Click here to register online.
Learning platform
Most of the courses in physics use the Athena learning platform. Once registered, the course should appear automatically in Athena. If you cannot find the course, contact the course coordinator. If the course uses a different website, you can find the link further down on this web page.
Conditionally admitted
If you are conditionally admitted to a course at our department you need to contact our Academic advisor before you can register. Contact us as soon as possible, well before the course starts. Contact details are found further down on this web page.
Applicants on waiting list
Are you placed on a waiting list to any of our courses? You will always be contacted via e-mail if you are offered a place. Normaly we will not admit new students if more than 1 week has passed after the first lecture.
Find the Departmend of Physics
Most of the physics courses are held in the AlbaNova building, located between the Frescati campus and the Royal Institute of Technology (Tekniska högskolan, KTH). Courses in medical radiation physics are sometimes held at Campus Karolinska Hospital. A few of our physics courses are also given in collaboration with KTH or other departments. If this is the case it is clearly stated further down on this web page.
Welcome activities
Stockholm University organises a series of welcome activities that stretch over a few weeks at the beginning of each semester. The programme is voluntary (attendance is optional) and includes Arrival Service at the airport and an Orientation Day, see more details about these events below.
Your department may also organise activities for welcoming international students. More information will be provided by your specific department.
Find your way on campus
Stockholm University's main campus is in the Frescati area, north of the city centre. While most of our departments and offices are located here, there are also campus areas in other parts of the city.
Read more
For new international students
In this course, you will learn that all matter and its interactions can be described in terms of quantum fields. In particular you learn about the theories of quantum electrodynamics, chromodynamics (strong interactions) and the electroweak theory. You will also learn how to calculate scattering amplitudes and cross sections.
The course begins with an introduction to the classical theory of fields in the Lagrangian and Hamiltonian formulations, and explores the fundamental relation between symmetries and conservation laws, as encoded in Noether's theorem. The quantum theory of fields is then developed, first, for non-interacting scalar fields, the Maxwell field and the Dirac field, clarifying the connection between quantum fields and elementary particles like photons and electrons. Then, to deal with interacting fields, the concepts of S-matrix expansion, scattering amplitudes and cross-sections, Feynman diagrams and rules, etc, are introduced and developed. Local gauge symmetry is introduced as the origin of all known interactions in nature. This directly leads to the theories of the electromagnetic force (quantum electrodynamics) and the strong nuclear force (quantum chromodynamics). To extend it to the weak force, we introduce spontaneous symmetry breaking and the Higgs mechanism as well as Yukawa couplings, and then formulate the unified
electroweak theory as an SU(2)xU(1) gauge theory. Finally, we introduce path integrals (or functional integrals) as an alternative formulation of quantum field theory.
Quantum field theory is used in many branches of physics. Hence, the course is recommended for master students who plan to pursue their studies in any branch of theoretical physics as well as students who plan to study experimental particles physics. The course is also recommended for PhD students in these areas who have not taken an equivalent course in their earlier studies.
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Course structure
This is a second cycle course given at half speed during daytime. This course can also be taken as a third cycle course.
More detailed information about the topics covered during this course can be found at the course webpage: Quantum Field Theory
Teaching format
The teaching consists of lectures and problem solving sessions.
Assessment
The examination on this course consists of two parts:
Exam: A written examination at the end of the course.
Homework problems: Written homework problems throughout the course.Examiner
Fawad Hassan
Phone: +468 5537 8739
E-mail: fawad@fysik.su.se
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Schedule
The schedule will be available no later than one month before the start of the course. We do not recommend print-outs as changes can occur. At the start of the course, your department will advise where you can find your schedule during the course. -
Course literature
Note that the course literature can be changed up to two months before the start of the course.
- F. Mandl och G. Shaw, Quantum Field Theory (2nd Edition)
- Classical Mechanics by H. Goldstein, C. P. Poole, J. L. Safko (chapter 13)
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Course reports
Här ligger ett skript.
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More information
When can I apply?
Registration is open from mid-March to mid-April for courses that run in the fall, and from mid-September to mid-October for courses that run in the spring.
Please note that many courses open for late registration in mid-July for courses in the autumn term and in mid-December for courses in the spring term.
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Contact
Course coordinator and teacher:
Fawad Hassan, tel: 08 5537 8739, e-mail: fawad@fysik.su.seExercises:
Nadia Flodgren, e-mail: nadia.flodgren@fysik.su.se
Joakim Flinckman, e-mail: joakim.flinckman@fysik.su.se
Dong Won Kim, e-mail: dongwon.kim@fysik.su.seAcademic advisor at the Department of Physics: studievagledare@fysik.su.se
Student office: studentexp@fysik.su.se
