## Curriculum

The course work is divided into four phases and is followed by a short research project, the essay. The full course will advance:

- Research Skills: problem formulation and solving, presentation skills and necessary background in computers and mathematics (Four weeks, full time).
- Core Topics: foundational subjects, such as quantum mechanics, relativity, field theory, statistical physics, dynamical systems, data analysis, and scientific computation. (Four three-week sessions, each with two courses running in parallel).
- Reviews: subdisciplinary subjects, such as particle physics, cosmology, quantum information, quantum foundations and condensed matter physics. Students will choose from a selection of courses (Three three-week sessions, each with three courses running in parallel. Students are required to take at least four review courses in order to meet course requirements).
- Explorations: short, in-depth courses on specialized fields which are currently "hot." Students will choose from a selection of courses (Three three-week sessions, each with three courses running in parallel. Students are required to take at least two exploration courses in order to meet course requirements).
- Essay: 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 remedial English courses, training in scientific writing, and presentation workshops.

Although all course grades are either Credit or No Credit, PSI's approach to evaluation involves continuous assessment throughout the year conducted by PSI's resident fellows and faculty. The goal is to encourage all students to achieve their potential and to avoid grade-chasing competition. The final grade on the PSI Certificate will be Pass or Fail.

## CORE COURSES

(Three weeks, 18 hours of lecture, 14 hours of tutorial)

**01. PSI Quantum Theory**

Schrodinger equation: free particle, harmonic oscillator, simple time dependent problems. Heisenberg picture and connection with classical physics. Entanglement and non-locality. Pure and mixed states, quantum correlators, measurement theory and interpretation.

**02. PSI Relativity**

Special relativity, foundations of general relativity, Riemannian geometry, Einstein's equations, FRW and Schwarzschild geometries and their properties.

**03. PSI Quantum Field Theory 1**

Canonical quantization of fields, perturbation theory, derivation of Feynman diagrams, applications in particle and condensed matter theory, renormalization in φ4.

**04. PSI Statistical Mechanics**

This course provides an introduction to Critical Phenomena in Statistical Mechanics. The main topics covered are phase diagrams, phase transitions, critical exponents, Mean Field Theory, Kadanoff lenght scaling, Block spin renormalization, the Renormalization Group Idea, Wilsonian RG, the ε - expansion. Advanced topics covered include finite size scaling, crossover phenomena and the Harris criterion.

**05. PSI Quantum Field Theory 2**

Feynman Path Integral, abelian and nonabelian gauge theories and their quantization, spontaneous symmetry breaking, nonperturbative techniques: lattice field theory, Wilsonian renormalization.

**06. PSI Condensed Matter**

The general principles guiding the course will be broken symmetries, phases and emergent collective modes.

## REVIEW COURSES

At least four of nine courses (Three weeks, 18 hours of lecture, 14 hours of tutorial):

**PSI Standard Model**

Application of Yang Mills theory to particle physics, QCD and its tests in the perturbative regime, theory of weak interactions, precision tests of electroweak theory, CKM matrix and flavour physics, open questions.

**PSI Cosmology**

Einstein’s equations and maximally symmetric solutions; the FRW metric; kinematics and dynamics of FRW, conformal time and horizons; the horizon and flatness problems; thermodynamics of the early universe; big bang nucleosynthesis; cosmic microwave background; the Standard Model of cosmology; dark matter and dark energy.

**PSI Quantum Foundations**

Operational and realistic approaches to the interpretation of quantm mechanics. Local realism and the EPR argument. Bell's theorem and non-locality. Contextuality and the Kochen-Specker theorem. The deBroglie-Bohm interpretation. The many world interpretation.

**PSI Quantum Gravity**

Linear gravity and gravitons. Gravitational path integral. Pertubative Lorentzian quantum gravity (QG) and the need for non-pertubative QG. Constrained Hamiltonian systems. Canonical formulation of GR. Non-pertubative canonical QG. The Wheeler-De Witt equation. Loop QG. Non-perturbative path-integral for gravity: lattice and discrete methods (Regge calculus) and causal dynamical triangulations (CDT). Surprises in non-perturbative approach.

**PSI Gravitational Physics Review**

Manifolds and tensors, differential forms, exterior and Lie derivatives, connections and curvature, Cartan's equations of structure, gravitational wave spacetime, warped compactification, (A)dS black holes, Euclidean method and Hawking temperature, cosmic strings and domain walls, C-metric, multi black hole solutions, Einstein Hilbert action, Brans-Dicke theory, black holes in higher dimensions, P-branes, Kaluza-Klein theory, KK black holes, Gauss-Codazzi formalism, Gibbons-Hawking term, black hole entropy, Israel's junction conditions, gravitational perturbation theory, counting physical degrees of freedom, beyond Einstein: large extra dimensions, Randall-Sundrum model.

**PSI Quantum Information Review**

Basic concepts: qubits, quantum gates, quantum circuits, density matrices, quantum operations, entropy, entanglement. Topics in quantum algorithms and complexity: languages, complexity classes, oracles, RSA, Deutsch-Jozsa algorithm, Shor's algorithm, Grover's algorithm. Information theory and implementations: overview of implementations, quantum error correction, quantum cryptography, quantum information theory.

**PSI String Theory**

Why string theory? Bosonic string: massless fields in curved spacetime, point particle and Polyakov actions, Nambu-Goto action, relativistic string, mode expansion, quantization, string spectrum, critical dimension, string theory as a theory of quantum gravity. Superstring: RNS formalism, spacetime fermions, critical dimension, Type IIA and IIB superstring theories, 11D Supergravity and its dimensional reduction, D-branes, T-duality, U(N) gauge group from superstrings, M-theory, 5 string theories and their dualities.

**PSI Condensed Matter Theory**

This class will cover the following topics: phase transitions, order parameters, Kosterlitz and Thouless phase transitions, quantum phase transitions, quantum XY model, entanglement, fidelity and Berry phases in QPTs, lattice gauge theories, confinement-deconfinement transitions, quantum and topological order, toric code and topological entropy.

**PSI Beyond the Standard Model**

Evidence and rationale for physics beyond the Standard Model: neutrinos, baryogenesis, dark matter, scale hierarchies, electro-weak precision experiments; BSM Physics: supersymmetry (a tale of unification), technicolor (superconductivity at the LHC), extra-dimensions (black holes, holography and strong coupling).

## EXPLORATIONS COURSES

At least two of six (three weeks, 18 hours of lecture, 14 hours of tutorial):

**PSI Explorations in Quantum Information**

Review of selected topics in Quantum Information.

**PSI Explorations in Condensed Matter Theory**

Review of selected topics in Condensed Matter Theory.

**PSI Explorations in String Theory**

Review of selected topics in String Theory.

**PSI Explorations in Cosmology**

Review of selected topics in Cosmology.

**PSI Explorations in Particle Theory**

Review of selected topics in Particle Theory.