From Path Integrals to Field Theory (honours)

Course manual 2025/2026

Course content

Path integrals and field theory stand at the core of modern theoretical physics, being universally used in areas ranging from condensed matter to high-energy physics. This course will provide an introduction to the fundamental concepts underlying the 'sum over histories' approach to quantum mechanics and its equivalent in classical systems. Path integrals will be introduced for single particles in quantum mechanics and in the context of classical Brownian motion, leading to a detailed exposition of the notion of propagators or Green's functions. Elements of scattering theory and of diagrammatic perturbation theory will be introduced. The generalization to field theory will be provided by considering simple many-body classical and quantum systems, including the atomic chain, Ising models and simple field equations, leading to diagrammatic methods for partition sums and correlation functions. 

Study materials

Other

• Notes will be provided by the teacher.

Objectives

• The understanding of the formulation of functional integrals for classical and quantum problems.
• The application of diagrammatic methods in perturbation and scattering theory.
• The calculation of partition functions and response functions of basic many-body systems.

Teaching methods

• Hoorcollege
• Werkcollege

Lectures and practical work.

Learning activities

Attendance

Programme's requirements concerning attendance (TER-B):

• Each student is expected to participate actively in each component of the programme that he/she signed up for. A student that does not attend the first two seminars of a course, will be administratively removed from the seminar group. A request for reregistration for the seminars can be applied to the programme coordinator.
• If a student cannot attend an obligatory component of a programme's component due to circumstances beyond his control, he must report in writing to the relevant teacher as soon as possible. The teacher, if necessary after consulting the study adviser, may decide to issue the student a replacing assignment.
• It is not allowed to miss obligatory commponents of the programme if there is no case of circumstances beyond one's control.
• In case of participating qualitatively or quantitatively insufficiently, the examiner can expel a student from further participation in the programme's component or a part of that component. Conditions for sufficient participation are set down in advance in the course manual.

Assessment

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Additional information

This course will be given in English.

Recommended prior knowledge: Quantumfysica 3 en Wiskunde N3.

Required prior knowledge: Statistische fysica, Wiskunde N2 en Elektrodynamica en relativiteitstheorie 2.

Contact information

Coordinator

• prof. dr. J.S. Caux