# Online courses

Perimeter Scholars International's **free **online learning modules enable motivated students and physics enthusiasts to study graduate-level theoretical physics independently at their own pace.

Each learning module contains a series of exercises and lecture notes designed to supplement recorded videos. The online program is free. Register to begin PSI Online.

### Quantum Field Theory I

This module introduces the canonical quantization of scalar, spinor, and abelian gauge fields. The Feynman diagram technique for perturbation theory is developed. Some applications in particle theory are discussed.

### Quantum Field Theory II

The Feynman path integral formulation of quantum mechanics is reviewed in this learning module. Its generalization to quantum field theory (functional integral quantization) is developed. Both the perturbative and Wilsonian approaches to renormalization and the renormalization group and their relation are discussed. Non-abelian gauge theories are quantized.

### Quantum Matter

This learning module begins with an overview of computational challenges in theories of many-body systems. Lattice Hamiltonians and exact diagonalization procedure are developed. The free particle formalism and its use as a guide in numerical simulations of many-body Hamiltonians is discussed. Entanglement and its structure in many-body wave-functions is explored. The learning module concludes by introducing tensor network states, including matrix product states and projected entangled pair states, and the multi-scale entanglement renormalization ansatz.

### Cosmology

This learning module provides an introduction to modern cosmology and how it explains some experimental facts about our Universe. We start by discussing the homogenous universe described by the FRW spacetime, explain the various components of the matter content, touch on Big Bang Nucleosynthesis, CMB, dark matter, and dark energy. We also discuss motivations for introducing inflation and how it predicts the right kind of fluctuations that lead to the structure formation in our Universe.

### Statistical Physics

The main goal of this learning module is to discuss phase transitions and critical phenomena in statistical physics. We introduce the ideas of mean field theory and renormalization group and exploit them to calculate the critical exponents for the Ising model. More advanced topics concern the models with continuous symmetry, topological phase transitions, as well as Monte Carlo simulations.

### Mechanics

This learning module provides a concise introduction to theoretical mechanics and its geometrical formulation in terms of symplectic and contact geometries. We review the basic concepts of action principle, Poisson brackets, and canonical transformations, as well as discuss more advanced topics such as the Hamilton-Jacobi theory, integrable systems, and constraints. No prior knowledge of differential geometry is expected.