Curriculum
The coursework is divided into two overlapping phases and a short research project in the form of an essay.
- Core Topics: foundational subjects — classical physics. quantum theory, relativity, quantum field theory, statistical physics, mathematical physics, numerical methods.
- Elective Courses: subdisciplinary subjects — such as particle physics, cosmology, quantum information, quantum foundations, and quantum matter physics — and courses on specialized fields which are currently "hot", such as Machine Learning for Many-Body Physics and AdS/CFT.
Each student undertakes a short research project supervised by a local or outside faculty member and produces an essay which is publicly presented and defended.
The program also includes English courses (if needed), training in science communication, and presentation workshops. As an example, the 2026/2027 schedule is below but it is subject to change:
Assessment
Although all course grades are either "credit" or "no credit," PSI's approach to evaluation involves assessment throughout the year conducted by academic staff. This assessment is in the form of oral interviews (for core courses), homework assignments, and contributions to tutorials. The goal is to encourage all students to achieve their potential and to avoid grade-chasing competition. All course grades are either credit or no credit.
PSI courses
September to February. The core courses cover foundational graduate-level subjects at an accelerated pace. Students take 6 out of the 7 core courses. The following are the descriptions of recent iterations of the core courses. Note that the courses and their topics are subject to change and may not fully reflect the content of the upcoming year.
Classical Physics
This course aims to review the basics of theoretical mechanics, special relativity, and classical field theory, with the emphasis on geometrical notions and relativistic formalism.
Quantum Theory
This course on quantum mechanics is divided in two parts:
The aim of the first part is to review the basis of quantum mechanics. The course aims to provide an overview of the perturbation theory to handle perturbations in quantum systems. Time evolution of quantum systems using the Schrodinger, Heisenberg and interaction pictures will be covered. Basics of quantum statistical mechanics for distinguishable particles, bosons, and fermions will be covered. A brief overview of the density matrix approach and quantum systems interacting with the environment will be given.
The second part of the course is an introduction to scalar quantum field theory. The Feynman diagram technique for perturbation theory is developed and applied to the scattering of relativistic particles. Renormalization is briefly discussed.
Quantum Field Theory I
The course starts by looking for a quantum theory that is compatible with special relativity, without assuming fields are fundamental. Nevertheless fields turn out to be a very good, maybe inevitable mathematical tool for formulating and studying such a relativistic quantum theory. The second part of the course introduces the Dirac theory and canonically quantizes it. It also quantizes the Maxwell field theory. The Feynman diagram technique for perturbation theory is developed and applied to the scattering of relativistic fermions and photons. Renormalization of quantum electrodynamics is done to one-loop order.
Relativity
This is an introductory course on general relativity (GR). We shall cover the basics of differential geometry and its applications to Einstein’s theory of gravity. The plan is to discuss black holes, gravitational waves, and observational evidence for GR, as well as to cover some of the more advanced topics.
Quantum Field Theory II
The course has three parts. In the first part of the course, the path integral formulation of non-relativistic quantum mechanics and the functional integral formulation of quantum field theory are developed. The second part of the course covers renormalization and the renormalization group. Finally, non-abelian gauge theories are quantized using functional integral techniques.
Statistical physics
The course begins by discussing several topics in equilibrium statistical physics including phase transitions and the renormalization group. The second part of the course covers non-equilibrium statistical physics including kinetics of aggregation, spin dynamics, population dynamics, and complex networks.
January to April. Elective courses introduce students to modern topics and cover cutting-edge research topics from various specialized subfields. The total number of elective courses changes each year, and is generally between twelve and fifteen. The following are the descriptions of elective courses from recent years. Note that the courses and their topics are subject to change and may not fully reflect the content of the upcoming year.
Recent courses and topics include:
Advanced GR
The main objective of this course is to discuss some advanced topics in gravitational physics and its applications to high energy physics. Necessary mathematical tools will be introduced on the way.
Quantum Matter
This course introduces key concepts in modern quantum matter, including spontaneous symmetry breaking, topological phases, and quantum criticality, illustrated through simple and instructive examples.
Quantum Foundations
This course will explain why textbook quantum “theory” is merely a mathematical recipe rather than a proper physical theory. It will then cover the most serious obstacles to fixing this problem and to providing a clear metaphysics underpinning the mathematics of quantum theory. We will focus on key no-go theorems (e.g., Bell’s theorem, contextuality theorems, and Extended Wigner’s friend arguments), as well as on key frameworks (e.g., generalized probabilistic theories and ontological models).
Quantum Information
We look to understand the possibilities and limits of quantum information processing, and how an information theory perspective can inform theoretical physics. Topics covered include: entanglement, tools for measuring nearness of quantum states, characterizing the most general possible quantum operations, entropy and measuring information, the stabilizer formalism, quantum error-correcting codes, the theory of computation, quantum algorithms, classical and quantum complexity.
Cosmology
FRW universe. Dark energy. Cosmic Microwave Background. Big Bang Nucleosynthesis. Dark Matter. LCDM cosmology. Inflation. Primordial perturbations. QFT in curved space background.
Scientific Machine Learning
This course introduces Scientific Machine Learning, beginning with an overview of traditional and modern machine learning methods illustrated with examples from physics. It then transitions to physics-informed approaches, where physical laws, symmetries, and mechanistic models are embedded into learning frameworks. Tutorials and assignments will emphasize developing programming skills in Python.
Quantum Fields and Strings
Advanced quantum field theory in lower dimension. The course will cover topics of advanced quantum field theory in lower dimension (d=2 or d=3) The topics may include string theory and/or integrability.
Quantum Gravity
We will study how General Relativity (GR) is similar to and especially how it differs from other gauge theories. This will explain why, from a structural perspective, it is much harder to quantize GR than other theories without relying on any specific approach to quantization. To achieve this goal, we will introduce the so-called “Covariant Phase Space Method” and use to study in detail the symmetry structure of GR and how it is intimately related to its dynamics. Along the way we will touch on (parts of) the historical debate on whether gravity should be quantized at all, discuss how to think of time evolution when there is no absolute time, and go through Wald’s proposal of black hole entropy as a Noether charge.
Standard Model
The course will give introduction into the structure of the Standard Model of particle physics and its field content. The emphasis will be made on the underlying principles, such as gauge invariance, cancellation of quantum anomalies, and Brout-Englert-Higgs mechanism. Effective low-energy description of strong interactions will be also discussed. It will be assumed that students are familiar with the basics of quantum field theory.
Mathematical Physics
We will study topics in theoretical physics through the lens of differential geometry and algebraic topology. The topics will be chosen among the following: differential forms on manifolds, homology, homotopy, de Rham cohomology, gauge theory and principal fiber bundles, nonperturbative effects and topology, characteristic classes, basics of solitons (ex: why is the instanton number a number?), index theorems, introduction to anomalies.
Quantum Field Theory III
The course will cover the basics of conformal field theories and some applications in 2 dimensions (Virasoro symmetry, conformal blocks, minimal models, Coulomb gas, c-theorem...)
The PSI program is supported by the Savvas Chamberlain Family Foundation, the Hellenic Heritage Foundation, the Marsland Family, and members of the Emmy Noether Circle.