# PSI Lectures/2011

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## Front[edit | edit source]

### Complex Analysis - Tibra Ali[edit | edit source]

- Lecture 1 - Review of the basics of complex numbers. Geometrical interpretation in terms of teh Argand-Wessel plane. DeMoivre's theorem and applications. Branch points and branch cuts.

- Lecture 2a Lecture 2b - Cauchy-Riemann equations. Holomorphic functions and harmonic functions. Contour integration.

- Lecture 3 - Cauchy's theorem and integral formula. Taylor's theorem. Singularities. Laurent's series. Residues.

- Lecture 4 - Applications of the integral formula to evaluate integrals. Trigonometric integrals, semi-circular contours, mousehole contours, keyhole contours.

### Linear Algebra - Anna Kostouki[edit | edit source]

- Lecture 1 - Linear Vector Spaces, Linear Operators, Scalar Products, Dual Spaces, Adjoint Operators, Eigenvalues Eigenvectors, Hermitian Unitary Operators.

- Lecture 2a Lecture 2b - Abstract Algebras, Structure Constants, Homomorphisms, Clifford Grassmann Algebras.

- Lecture 3 - Group Theory: Finite groups and the permutation group. SU(2) and SO(3).

- Lecture 4 - The Lorentz and Poincaré groups (a short review of Special Relativity).

### Differential Equations - Sarah Croke[edit | edit source]

- Lecture 1 - First order differential equations; examples: Einstein theory of radiation, optical attenuations; methods of solution.

- Lecture 2 - Second order differential equations, homogeneous and inhomogeneous; reduction of order; variation of parameters; the Wronskian.

- Lecture 3 - Series solutions; Euler's equation; Extended power series method, form of solutions in different cases; Bessel's equation.

- Lecture 4 - Bessel Functions; Separation of variables; Spherical Harmonics; WKB approximation.

### Evaluation of Integrals and Calculous of Variations -Denis Dalidovich[edit | edit source]

- Lecture 1 - Gaussian Integrals in one and many dimensions. Averages with the Gaussian weight.

- Lecture 2 - Wick's Theorem. Imaginary Gaussian Integral. Gaussian Integral with Grassman variables.

- Lecture 3- Functionals and functional derivatives. Euler-Lagrange equations; examples from classical mechanics.

- Lecture 4 - Noether's theorem. Functionals describing continuous systems; Lagrangian density. Extrema of functionals subject to contraints; Lagrange multipliers.

### Special Functions and Distributions - Dan Wohns[edit | edit source]

- Lecture 1 - Dirac delta; Test functions; Distributions and their derivatives.

- Lecture 2 - Orthogonal polynomials; Recurrence relations; Weights.

- Lecture 3 - Generalized Rodrigues' formulae; Classification of orthogonal polynomials; Sturm-Liouville theory.

- Lecture 4 - Gamma; Zeta; Hypergeometric functions

### Integral Transforms and Green's Functions - David Kubiznak[edit | edit source]

- Lecture 1 - Fourier Series

- Lecture 2 - Laplace Fourier transform

- Lecture 3 - Green's functions

- Lecture 4 - Applications

### Lie Groups and Lie Algebra's - Freddy Cachazo[edit | edit source]

- Lecture 1 - Introduction to Lie Groups and Lie Algebras in Physics. Lie groups, representations, structure constants.

- Lecture 2 - The Poincaré group algebra. Representations on Hilbert space. Massless and massive irreps. The Little Group.

- Lecture 3 - Classifications of Lie Algebras. Helicity and Spin. Highest weight representations of SU(2).

- Lecture 4 - The Adjoint representation. Classification of (simple) Lie Algebras. Roots diagrams and Dynkin diagrams.

- Lecture 5 - The group associated with the standard model of particle physics. Weights. Highest weight representations. Fundamental and anti-fundamental representations of su(3). Tensor products of representations. Clebsch-Gordan Decomposition. Young's Tableaux.

### Mathematica - Pedro Vieira[edit | edit source]

- Lecture 1 - Mathematica Basics

- Lecture 2 - Heisenberg Spin Chain

- Lecture 3 - Gamma Matrices

- Lecture 4 - Harmonic Oscillator and Perturbation Theory

- Lecture 5 - Q A Session

### RESEARCHER PRESENTANTIONS:[edit | edit source]

- Presentation 1 - Paul Fendley
- Presentation 2 - Joseph Minahan
- Presentation 3 - Matthias Staudacher
- Presentation 4 - Yakir Aharonov
- Presentation 5 - Vladimir Kazakov
- Presentation 6 - Itay Yavin
- Presentation 7 - Guifre Vidal
- Presentation 8 -Lucien Hardy
- Presentation 9 - Laurent Freidel
- Presentation 10 - Robert Spekkens
- Presentation 11 - Lee Smolin
- Presentation 12 - Cliff Burgess
- Presentation 13 -Avery Broderick
- Presentation 14 - Pavel Kovtun
- Presentation 15 - Subir Sachdev

## Core[edit | edit source]

### Quantum Theory - Adrian Kent[edit | edit source]

- Lecture 1 - Gaussian wave-packets, double-slit experiment, tension with special relativity.

- Lecture 2 - Unitary evolution, Path integrals.

- Lecture 3 - Discussion of path integral. Problems deriving classical physics from quantum theory.

- Lecture 4 - Feynman checkerboard model, Angular momentum.

- Lecture 5 - Spin, Bloch sphere, Quantum Zeno effect, Mixed states.

- Lecture 6 - Guest Lecturer: Lucien Hardy. Interferometry, Elitzur-Vaidman bomb tester.

- Lecture 7 - Guest Lecturer: Lucien Hardy. Quantum-optical interferometry, Ou-Hong-Mandel effect.

- Lecture 8 - Guest Lecturer: Rafael Sorkin. The quantum measure. Three-slit experiment. Classical action.

- Lecture 9 - Guest Lecturer: Rafael Sorkin. Mathematical details of the quantum measure. Unitarity.

- Lecture 10 - Density matrices - definition and properties. Mixed states on the Bloch sphere. Proper and improper mixtures.

- Lecture 11 - Entanglement. Partial trace. No-signaling.

- Lecture 12 - EPR argument. Bell-CHSH inequalities. Experimental tests.

- Lecture 13 - Hidden variables. Extensions of Bell-CHSH inequalities. No cloning.

- Lecture 14 - Approximate cloning. Quanutm money.

- Lecture 15 - Measurements in QM. Kraus operators. Decoherence. Many-worlds.

### Relativity - Neil Turok[edit | edit source]

- Lecture 1 - Maxwell's Theory and Special Relativity.

- Lecture 2 - Lorentz Transformations.

- Lecture 3 - Manifolds.

- Lecture 4 - Tensors and Manifolds.

- Lecture 5 - The Connection.

- Lecture 6 - Geodesics, The Reimann Tensor.

- Lecture 7 - Tensors in GR.

- Lecture 8 - Action for relativistic particle, Einstein's equations.

- Lecture 9 - The Stress Energy Tensor of a perfect fluid in GR, the Einstein - Hilbert Action, spherically symmetric solutions of Einstein's equations.

- Lecture 10 - Schwarzschild solution, crossing the horizon, Krustal extension.

- Lecture 11 - Schwarzschild solution, crossing the horizon, Krustal extension.

- Lecture 12 - Particles in Schwarzschild, Precession of the Perihelion.

- Lecture 13 - Rotating Black Hole (Kerr solution), Event horizons.

- Lecture 14 - Causal Diagrams, Cosmological Solutions: maximally symmetric spaces, Friedmann equations.

- Lecture 15 - Causal Diagrams, Cosmological Solutions: maximally symmetric spaces, Friedmann equations

### Quantum Field Theory I - Konstantin Zarembo[edit | edit source]

- Lecture 1a Lecture 1b - Second Quantization, Phonons.

- Lecture 2 - Phonons, Divergences.

- Lecture 3 - Klein-Gordon field, Conservation laws and symmetries.

- Lecture 4 - Noether's theorem, Quantization of Klein-Gordon field, Dirac equation.

- Lecture 5a Lecture 5b - Lorentz invariance and symmetries of Dirac Lagrangian.

- Lecture 6 - Solutions of the Dirac equation, Quantization of the Dirac field.

- Lecture 7 - Weyl fermions, Electromagnetic Field, Gauge transformations.

- Lecture 8 - Quantum Electrodynamics, Perturbation Theory.

- Lecture 9 - Response to Students' Questions, Dimensional Analysis.

- Lecture 10 - Interaction Picture.

- Lecture 11 - Wick's Theorem, Feynman Diagrams.

- Lecture 12 - Feynman Propagator, Momentum Space Feynman Rules

- Lecture 13 - Amplitudes, Cross Sections, Decay Rates.

- Lecture 14 - QED Feynman rules, the Coulomb potential, Yukawa theory.

### Statistical Mechanics - Leo Kadanoff[edit | edit source]

- Lecture 1 - Introduction to statistical physics phenomena, Partition function.

- Lecture 2 - Partition functions: means and variances. Non-interacting particles in a box.

- Lecture 3 - Pressure of an ideal gas. One-Dimensional Ising model: exact solution.

- Lecture 4 - One-dimensional Ising model: correlation length and solution by renormalization.

- Lecture 5 - Two-dimensional Ising model: phase transitions.

- Lecture 6 - Hopping on a lattice and diffusion equation.

- Lecture 7 - Diffusion in momentum space. Brownian motion. Hamiltonian Dynamics.

- Lecture 8 - Statistical ensambles, Stochastic processes, Fokker-Planck equation.

- Lecture 9 - Boltzmann equation.

- Lecture 10 - H-theorem. Kinetic equation for Fermi/Bose gases.

- Lecture 11 - Van-der-Vaals equation. The notion of a phase transition.

- Lecture 12 - Phase transitions, Mean field theory, Landau's theory.

- Lecture 13 - Limitations of the mean field theory, Fluctuations.

- Lecture 14 - Scaling and renormalization group.

### Quantum Field Theory II - François David[edit | edit source]

- Lecture 1 - Path Integral, Euclidean Time.

- Lecture 2 - Semi-classical Expansion, Free Scalar Field.

- Lecture 3 - Feynman propagator, Wick's Theorem, Interactions.

- Lecture 4 - Feynman Diagrams, Generating Functionals, Loop Expansion.

- Lecture 5 - Effective Action at One Loop.

- Lecture 6 - Renormalization of Phi^4 Theory.

- Lecture 7 - Renormalization of the coupling constant in massless Phi^ Theory, Renormalization Group.

- Lecture 8 - Renormalization of the massless Phi^4, Operator Product Expansion.

- Lecture 9 - Wilsonian Renormalization.

- Lecture 10 - Renormalization Group Flow, Grassman Variables, Berezin Claculus.

- Lecture 11 - Berezin Calculus, Fermionic Path Integrals.

- Lecture 12 - Non-abelian Gauge Theories.

- Lecture 13 - Quantization of Non-abelian Guage Theories, Guage Fixing, Faddeev-Popov Method.

- Lecture 14 - Faddeev-Popov Lagrangian, Ghosts.

- Lecture 15 - Renormalization of Guage Theories, Dimensional Regularization, Asymptotic Freedom, Lattice Guage Theories.

### Condensed Matter - Nandini Trivedi[edit | edit source]

- Lecture 1 - Basic ideas of Condensed Matter. Crystals, Bravais and reciprocal lattices, x-ray scattering, density-density correlations.

- Lecture 2 - Collective modes of a crystal, dynamical matrix; mode quantization and phonons; thermodynamics of phonons and specific heat.

- Lecture 3 - Symmetry breaking, long-range order and Goldstone modes; structure factor and Debye-Waller factor.

- Lecture 4 - Quantum Indistinguishability; Fermi gas and the notion of Fermi liquid; Bose gas and Bose-Einstein condensation.

- Lecture 5 - Electron-electron interactions and magnetism; Hund's rule; singlet-triplet splitting; spin Hamiltonian.

- Lecture 6 - Heisenberg Hamiltonian and symmetry breaking; Ferromagnetism: ground state and excitations (spin waves); Antiferromagnetic state.

- Lecture 7 - Antiferromagnets: spin singlets, RVB states, spin liquids in various dimensions; Schwinger boson approach; weakly interacting Bose gas.

- Lecture 8 - Interacting Bose gas: Bogoliubov transformation, energy spectrum, ground state energy, depletion of the condensate.

- Lecture 9 - Off-diagonal long-range order, phase fluctuations of condensate; Bose-Hubbard model, quantum phase transition.

- Lecture 10 - Properties of superfluids and the phase diagram of He-4; vortices and Berenzinskii-Kosterlitz-Thouless transition.

- Lecture 11 - Properties of superconductors; Cooper instability; Bardeen-Cooper-Schrieffer Hamiltonian.

- Lecture 12 - BCS theory: spectral function, density of states, gap equation, calculation of the critical temperature.

- Lecture 13 - Ginzburg-Landau theory: solutions for a bulk superconductor and superconductor with a boundary. London penetration depth and flux quantization.

- Lecture 14 - Vortices in superconductors; type-1 and type-2 superconductors: Abrikosov vortex lattice; Josephson effect.

- Lecture 15 - Josephson junction in a magnetic field.

### Mathematical Physics - Carl Bender[edit | edit source]

- Lecture 1 - Perturbation series. Brief introduction to asymptotics.

- Lecture 2 - The Schroedinger equation. Riccati equation. Initial value problem. Perturbation series approach to solving the Schroedinger equation. The eigenvalue problem.

- Lecture 3 -Putting a perturbative parameter in the exponent. Thomas-Fermi equation. KdV equation. Eigenvalue problem - analytic structure of the energy function. The square root function. Branch cuts. Shanks transform.

- Lecture 4 - Acceleration of convergence. Shanks transform. Richardson extrapolation. Summing a divergent series. Euler summation. Borel summation. Generic summation machines.

- Lecture 5 - Summation of divergent series continued. Analytic continuation of zeta and gamma functions. The anharmonic oscillator.

- Lecture 6 - Continued fractions. Pade sequence. Stieltjes series.

- Lecture 7 - Pade technique for summing a series. Asymptotic series. Fuchs' theorem. Frobenius series.

- Lecture 8 - Local analysis. Asymtotic series solution to differential equations continued. WKB approximation.

- Lecture 9 - Asymptotic series solution to differential equations continued. Optimal asymptotic approximation. Airy functions. Stokes phenomenon.

- Lecture 10 - Asymptotic solutions to the inhomogeneous Airy equation. The rigourous theory of asymptotics. Stieltjes functions. The four properties of Stieltjes functions. Herglotz property.

- Lecture 11 - Proof of Herglotz property of Stieltjes functions. Stieltjes functions and the convergence of Pade sequences. The moment problem. Carleman condition. The anharmonic oscillator as an example of Carleman condition.

- Lecture 12 - Asymptotic distribution of the number of Feynman diagrams in phi^4 theory. Comparison with phi^6 and phi^8 theories. Sketch of the precise asymptotic expression for the coefficient of the perturbation theory.

- Lecture 13 - Accuracy of WKB. Solution to the Sturm-Liouville problem using WKB. Turning points. Trajectories in complex classical mechanics.

- Lecture 14 - Asymptotic solution to the Sturm-Liouville problem for two turning points. Asymptotic matching.

- Lecture 15 - Solution to the two turning-point problem. Examples: the harmonic oscillator. V(x) = x^4. A brief introduction to hyper asymptotics.

### Conformal Field Theory -Jaume Gomis[edit | edit source]

- Lecture 1 - Introduction to CFTs (1): Conformal invariance of classical actions, RG flows and fixed points, classification of operators.

- Lecture 2 - Introduction to CFTs (2): Critical phenomena in statistical physics, phase transitions.

- Lecture 3 - Conformal Transformations Conformal Algebra.

- Lecture 4 - Conserved currents and the Stress Energy Tensor.

- Lecture 5 - Conformal Anomalies, Conformal Operators and Fields.

- Lecture 6 - Conformal Fields contiued: Primaries and Descendants.

- Lecture 7 - Correlation Functions in CFTs.

- Lecture 8 - Correlators of Vectors and Tensors; D=2 CFTs: the complex plane, the de Witt algebra.

- Lecture 9 - Primary and quasi-primary Operators, Correlators and the Stress Tensor in D=2.

- Lecture 10 - Operator Product Expansion, Ward Identities, Virasoro Algebra.

- Lecture 11 - Hilbert Space in CFTs, Primaries and descendants.

- Lecture 12 - Operator/State Correspondence, Unitarity Bounds on CFTs.

- Lecture 13 - Minimal models in D=2; Null vector decoupling equation.

- Lecture 14 - Fusion rules; The Ising model in D=2.

## Review[edit | edit source]

### Standard Model (Review) - Philip Schuster, Natalia Toro[edit | edit source]

- Lecture 1 - Particle Bestiary.

- Lecture 2 - Quark Model, Standard Model Langrangian.

- Lecture 3 - Standard Model Lagrangian.

- Lecture 4 - Standard Model Lagrangian after Electroweak Symmetry Breaking.

- Lecture 5 - Little Group, Single Particle States, Multi-Particle States.

- Lecture 6 - Lorentz Transformation of Multi-Particle States, Fields from the S-Matrix, Spin-Statistics.

- Lecture 7 - Particle Number Violation and Antiparticles, Effective Field Theories.

- Lecture 8 - Effective Field Theories, Sigma Model.

- Lecture 9 - Chiral Symmetry Breaking, Goldstone Bosons, Sigma Model for Pions.

- Lecture 10 - Pions as Pseudo-Nambu-Goldstone Bosons.

- Lecture 11 - Light meson masses, Pion Decays.

- Lecture 12 - Jets, Altarelli-Parisi Splitting Functions.

- Lecture 13 - Higgs Mechanism.

- Lecture 14 - Massive Vector Bosons and Unitarity.

- Lecture 15 - Higgs Searches.

### Condensed Matter (Review) - Alioscia Hamma[edit | edit source]

- Lecture 1 - Outline of the course. Phase transitions, critical points, scaling, the role of dimensionality. The concepts of phase and symmetry.

- Lecture 2 - Review of the Ising model. Solidification transition. Transfer matrix formalism.

- Lecture 3 - Correlation functions. The correspondence between statistical and quantum mechanics. The notion of a quantum phase transition.

- Lecture 4 - Transverse Ising Model in one-dimension: ground state, quantum critical point, duality argument, exact solution using Jordan-Wigner transformation.

- Lecture 5 - Locality in quantum soin systems. Lieb-Robinson theorem.

- Lecture 6 - Lieb-Robinson bounds: Consequences of locality; effective light cone and the spread of information, bounds on correlation functions.

- Lecture 7 - Fidelity, quantum geometric tensor; Berry phases in an XY chain.

- Lecture 8 - Quantum geometric tensor near quantum phase transitions and for 1D Ising chain; the notion of entanglement.

- Lecture 9 - Entanglement in many body systems, von Neumann entropy and the role of dimensionality; Lattice Z_2 guage model and Elitzur's theorem.

- Lecture 10 - Phase transition in lattice Z_2 gauge model. Quantum lattice Z_2 guage theory, guage transforamtions.

- Lecture 11 - Gauge-invariant Hilbert space in Z_2 guage theory; the notion of topological quantum order.

- Lecture 12 - Toric code. String-net condensation.

- Lecture 13 - Entanglement in topologically ordered ground state. Quantum double model.

- Lecture 14 - Topological quantum phase transitions.

- Lecture 15 - Lattice U(1) guage theory and emergent photons.

### Foundations of Quantum Mechanics (Review) - Rob Spekkens[edit | edit source]

- Lecture 1 - What's the problem? The realist strategy. The quantum measurement problem.

- Lecture 2 - The operational strategy. The most general types of preparations. Density operators.

- Lecture 3 - Operational quantum mechanics. The most general types of measurements. The most general types of transformations.

- Lecture 4 - POVMs. Unambiguous state discrimination. Operational formulation of quantum theory. The church of the larger (smaller) Hilbert space.

- Lecture 5 - A framework for convex operational theories. Operational classical theory. Operational quantum theory. Real vs complex field.

- Lecture 6 - Recasting the "orthodox" interpretation as a realist model. Realism via hidden variables. Psi-ontic vs psi-epistemic models. The Bell-Mermin model. The Kochen-Specker model.

- Lecture 7 - Evidence in favour of psi-epistemic hidden variable models. Restricted Liouville mechanics. Restricted statistical theory of bits.

- Lecture 8 - Bell's theorem. Experimental loopholes. No-signalling.

- Lecture 9 - Non-locality. Bell's definition of local causality. Applications of non-localtiy. Contextuality.

- Lecture 10 - Contextuality in more depth. The traditional definiton of contextuality in quantum theory. Bell-Kochen-Specker theorem. Proofs of noncontextuality. An operational notion of contextuality.

- Lecture 11 - Generalized notions of noncontextuality. Preparation noncontextuality. Operational test of preparation noncontextuality. Connection with nonlocality. Noncontextuality and negativity as notions of classicality.

- Lecture 12 - The deBroglie-Bohm interpretation. The deBroglie-Bohm interpretation for a single particle. Empty waves and occupied waves. The deBroglie-Bohm interpretation for many particles. Effective collapse of the guiding wave.

- Lecture 13 - The deBroglie-Bohm interpretation continued. The "standard distribution" as quantum equilibrium. Contextuality. Criticisms and responses.

- Lecture 14 - Dynamical collapse theories. The Ghirardi-Rimini-Weber model. Constraints on parameters. Criticisms.

- Lecture 15 - The Everett interpretation - "Many Worlds." Preferred basis problem. The problem with probabilities. Comparison to deBroglie-Bohm.

### Quantum Gravity (Review) - Renate Loll[edit | edit source]

- Lecture 1 - Introduction to the subject of quantum gravity.

- Lecture 2 - Weak gravitational waves.

- Lecture 3 - Quantization of gravitational waves.

- Lecture 4 - Detectability of gravitational waves. Review of path integral in quantum mechanics.

- Lecture 5 - Perturbative path integral for gravity. Graviton propagator.

- Lecture 6 - Review of Hamiltonian mechanics. Dirac's conanonical quantization.

- Lecture 7 - Constrained Hamiltonian systems.

- Lecture 8 - Canonical Formulation of general relativity, ADM decomposotion. Dirac-Bergmann algorithm.

- Lecture 9 - Dirac algebra. Quantizing constrained systems.

- Lecture 10 - Dirac quantization for gravity. Wheeler-DeWitt equations.

- Lecture 11 - The notion of loop quantum gravity.

- Lecture 12 - Non-perturbative gravitational path integral.

- Lecture 13 - Dynamical triangulations and quantum Regge calculus.

- Lecture 14 - Path Integral in terms of dynamical triangulations. Monte-Carlo simulations for path integral.

- Lecture 15 - Casual dynamical triangulations.

### Gravitational Physics (Review) - Ruth Gregory[edit | edit source]

- Lecture 1 - Manifolds and Tensors.

- Lecture 2 - Differential Forms, Exterior and Lie Derivatives.

- Lecture 3 - Connections and Curvature, Cartan's Equations of Structure.

- Lecture 4 - Examples: Gravitational Wave Spacetime, Warped Compactification.

- Lecture 5 - (A)dS Black Holes, Eucliean Method and Hawking Temperature.

- Lecture 6 - Cosmic Strings and Domain Walls.

- Lecture 7 - C-Metric, Multi Black Hole Solutions.

- Lecture 8 - Einstein Hilbert Action, Brans-Dicke Theory.

- Lecture 9 - Black Holes in Higher Dimensions, P-Branes.

- Lecture 10 - Kaluza-Klein Theory, KK Black Holes.

- Lecture 11 - Gausse-Codazzi Formalism.

- Lecture 12 - Gibbons-Hawking Term, Black Hole's Entropy.

- Lecture 13 - Israel's junction Conditions.

- Lecture 14 - Gravitational Perturbation Theory, Counting Physical Degrees of Freedom.

- Lecture 15 - Beyond Einstein: Large Extra Dimensions, Randall-Sundrum Model.

### Cosmology (Review) -Latham Boyle[edit | edit source]

- Lecture 1 - Review of General Relativity

- Lecture 2 - Review of General Relativity continued, General Relativity and Yang-Mills Theory.

- Lecture 3 - Einstein's equation and maximally symmetric solutions.

- Lecture 4 - Maximally symmetric space-times; FRW.

- Lecture 5 - Kinematics of FRW, conformal time, horizons.

- Lecture 6 - The Horizon Problem, Dynamics of FRW.

- Lecture 7 - The Flatness Problem. Thermodynamics, Statistical Mechanics, Particle Physics.

- Lecture 8 - Big Bang Nucleosynthesis (BBN) and Cosmic Microwave Background (CMB) part 1.

- Lecture 9 - Big Bang Nucleosynthesis (BBN) and Cosmic Microwave Background (CMB) part 2.

- Lecture 10 - The Standard Model of Cosmology.

- Lecture 11 - Dark Matter and Dark Energy.

- Lecture 12 - Dark Matter and Dark Energy continued.

- Lecture 13 - Baryogenesis.

- Lecture 14 - Ifnlation

- Lecture 15 - Ifnlation continued.

### Quantum Information (Review) - Daniel Gottesman[edit | edit source]

- Lecture 1 - Classical gates. Reversible classical gates. Quantum gates.

- Lecture 2 - Universal gate sets. CP-maps. Purification.

- Lecture 3 - Implementations. Ion trap implementation.

- Lecture 4 - Comparison of implementations. Dynamical decoupling.

- Lecture 5 - Computational complexity. Complexity classes.

- Lecture 6 - Strong Church-Turing thesis. Complexity classes BQP and NP. Deutsch-Josza algorithm

- Lecture 7 - Factoring. RSA. Shor's algorithm.

- Lecture 8 - Shor's algorithm. Quantum Fourier transform.

- Lecture 9 - Grover's algorithm.

- name=Daniel_Gottesman Lecture 10 - Distance measures. Entropy.

- Lecture 11 - Compression. Mixed state entanglement.

- Lecture 12 - Quantum error-correcting codes.

- Lecture 13 -Stabilizer codes. Fault-tolerance

- Lecture 14 - Quantum key distribution

### String Theory (Review) - Freddy Cachazo[edit | edit source]

- Lecture 1 - Why String Theory? Historical Introduction

- Lecture 2 - Massless Fields in Curved Spacetime, Point Particle and Polyakov Actions

- Lecture 3 - Relativistic Strings: Equations of Motion, Constraints, Boundary Conditions.=

- Lecture 4 - Closed Strings: Mode Expansion and Quantization

- Lecture 5 -Quantizing Open Strings: String Spectrum, Critical Dimension

- Lecture 6 -String Theory as a Theory of Quantum Gravity

- Lecture 7 -String Theory as a Theory of Quantum Gravity

- Lecture 8 - by Lilia Anguelova - 11D SUGRA

- Lecture 9 - by Lilia Anguelova - IIA String Theory from Dimensional Reduction of 11D SUGRA

- name=Freddy_Cachazo Lecture 10 - RNS Formalism

- Lecture 11 - Superstrings: Spacetime Fermions, Critical Dimensions

- Lecture 12 - Type IIA and IIB Superstring Theories

- Lecture 13 - D-branes, T-duality, U(N) Gauge Group from Superstrings

- Lecture 14 -M-Theory and 5 String Theories

### Beyond the Standard Model (Review) - Veronica Sanz[edit | edit source]

- Lecture 1 - Intro to BSM. Evidence BSM: a)Dark Matter. Direct and indirect detection.

- Lecture 2 - b) Baryogensis. Sakharov conditions. c) Neutrino masses.

- Lecture 3 - Theoretical rationale for BSM. Technical naturalness. Gauge hierarchy problem.

- Lecture 4 -Explicit symmetry breaking and spontaneously broken symmetry. Other hierarchies in the Standard Model.

- Lecture 5 - Direct and Indirect constraints on BSM. The Peskin-Takeuchi S, T, U parameters. Flavour bounds. Forward-backward asymmetry.

- Lecture 6 -Supersymmetry. Coleman-Mandula no-go theorem. The Haag-Lopuszanski-Sohnius theorem. Chiral supermultiplet and the Wess-Zumino model

- Lecture 7 - Supersymmetric interactions. MSSM. Quadratic divergence in higgs mass. Cancellation of quadratic divergences from supersymmetric vertices.

- Lecture 8 - Soft SUSY breaking terms. The mu-problem. SUSY particle spectrum.

- Lecture 9 - Mass spectrum of MSSM. Dark matter candidate and gauge unification.

- Lecture 10 - SUSY breaking. Spontaneous SUSY breaking. Sum rule. SUSY breaking mediated by gravity, gauge sector and gauginos.

- Lecture 11 - Extra dimensions as a way of stabilizing the electroweak scale.

- Lecture 12 - Large extra dimensions continued. KK mechanism. ADD mechanism.

- Lecture 13 - Warped extra dimensios. The Randall-Sundrum scenario.

- Lecture 14 - Higgs searches at the LHC. SUSY searches at the LHC.

## Exploration[edit | edit source]

### Explorations in Quantum Information - David Cory[edit | edit source]

- Lecture 1 - Neutron interferometry. Ideal case.

- Lecture 2 - Imperfections. Superoperators, CP maps.

- Lecture 3 - Bloch equations. Noise: composite pulse sequence; magnetic fields in neutron interferometry.

- Lecture 4 -Imperfections. Wedge in one path. Imperfect blades.

- Lecture 5 - Imperfections. Velocity impared to / from blade.

- Lecture 6 -Spin degree of freedom in NI

- Lecture 7 - NV centres in diamond. Physical system. Initialization and measurement.

- Lecture 8 - Spin exchange interaction

- Lecture 9 - The rotating-wave approximation. Entanglement between NV centres.

- Lecture 10 - Hamiltonians and control of electron-nucker spin system.

- Lecture 12 - Superconducting rings. Josephson junction.

- Lecture 13 - Finite difference method. Eigenstructure of tilted potential for JJ circuit.

- Lecture 14 - Adding a parabolic potential to the JJ circuit. Mapping a Qubit. Hamiltonians and control of system.

- Lecture 15 - DiVincenzo criteria for superconducting qubit. 2-qubit circuit and control

### Explorations in Cosmology - Matthew Johnson,Louis Leblond[edit | edit source]

- Lecture 1 - Review of the standard model of cosmology

- Lecture 2 - QFT om curved space

- Lecture 3 - Unruh effect

- Lecture 4 -Unruh effect and particle production. de Sitter space.

- Lecture 5 - Scalar field fluctuations in de Sitter space. Inflationary models.

- Lecture 6 - Inflation: the homogeneous limit.

- Lecture 7 - Example:Chaotic inflation. Density perturbations produced during slow-roll inflation.

- Lecture 8 - Spectral index. Observational constraints on chaotic inflation. Gauges for scalar perturbations. Sachs-Wolfe effect.

- Lecture 9 - Connecting the primordial power spectra to CMB observables. Stochastic eternal inflation.

- Lecture 10 - Stochastic eternal inflation and the Fokker-Planck equation. Introduction to vacuum decay in QFT.

- Lecture 11 - Vacuum decay in CM.

- Lecture 12 - Vacuum decay in QFT.

- Lecture 13 - Vacuum decay with gravity. False vacuum eternal inflation.

- Lecture 14 - False vacuum eternal inflation. Quantum cosmology and wave function of the universe.

- Lecture 15 - Challenges for inflation. Alternatives to inflation.

### Explorations in String Theory - Pedro Vieira[edit | edit source]

- Lecture 1 - Introduction to the duality between string theory and large N gauge dualities

- Lecture 2 - Large N theories are simpler

- Lecture 3 - The decoupling argument and the AdS/CFT conjecture

- Lecture 4 - More arguments pointing towards AdS/CFT

- Lecture 5 - N=4 SYM; Wilson loops

- Lecture 6 - The quark-antiquark potential, Wilson loops in QED and in non-abelian gauge theories

- Lecture 7 - Minimal surfaces in AdS

- Lecture 8 - Supersymmetric Wilson loops, rainbow diagrams; Recent developments: Localization, Integrability, Null Polygon Wilson Loops

- Lecture 9 - Conformal Field Theory: 2, 3 4-pt functions, the Operator Product Expansion, the Conformal Bootstrap

- Lecture 10 - AdS geometry; Pointlike string solution in AdS5xS5

- Lecture 11 - Circular rigid sting solution; Computation of anomalous dimensions in N=4 SYM

- Lecture 12 - N=4 SYM and Heisenberg Spin Chains

- Lecture 13 - Spin Chains: single and N-magnon excitations, Bethe ansatz

- Lecture 14 - Bethe ansatz, the circular string and the single cut solutions

- Lecture 15 -Higher loop corrections, thermodynamic Bethe ansatz

### Explorations in Quantum Gravity - Carlo Rovelli[edit | edit source]

- Lecture 1 - Quanta of space.

- Lecture 2 - What is quantum gravity

- Lecture 3 - Hamilton's function, Physics without time

- Lecture 4 - Quantum physics without time

- Lecture 5 - Classical GR in tetrad formalism

- Lecture 6 - Euclidean 3D gravity

- Lecture 7 - Math of SU(2)

- Lecture 8 - Ponzanno-Regge transition amplitude

- Lecture 9 - Towards real quantum world

- Lecture 10 - by Eugenio Bianchi - Spectrum of the volume operator

- Lecture 11 - by Eugenio Bianchi - Coherent states, Unitary representations of SL(2,C)

- Lecture 12 - Quantum dynamics in 4D

- Lecture 13 - Properties of the full theory

- Lecture 14 - Physical applications and future directions

### Explorations in Particle Theory - David Morrissey[edit | edit source]

- Lecture 1 - Evidence for dark matter (DM). DM properties. Outline of course.

- Lecture 2 - Dark matter and structure.

- Lecture 3 - DM production. Thermodynamic equilibrium. The Boltzmann equation.

- Lecture 4 - Freeze out. Solving the Boltzman equation. The WIMP miracle.

- Lecture 5 - LSP as WIMP.

- Lecture 6 - Models of Non-thermal DM.

- Lecture 7 - Direct detection of DM.

- Lecture 8 - Direct detection continued. Spin independent and spin

- Lecture 9 - Spin independent experimental searches: XENON100, CDMS, DAMA, CoGeNT, CRESST

- Lecture 10 - Indirect detection of DM

- Lecture 11 - Indirect detection continued.

- Lecture 12 - Indirect detection: photon signal; DM in stars

- Lecture 13 - DM signals at colliders. Axions

- Lecture 14 - Axions and the Strong CP problem. Axion cosmology.

### Explorations in Numerical Relativity - Luis Lehner, Frans Pretorius[edit | edit source]

- Lecture 1 - Finite difference technique.

- Lecture 2 - Solutions of the wave equation using Crack-Nicholson algorithm; error evaluation and the problem of stability

- Lecture 3 - Arnowitt-Deser-Misner decomposition

- Lecture 4 - Gauss-Codazzi equations; 3+1 Approach to the Einstein Equations

- Lecture 5 - Hyperbolic equations; linearly degenerate vs truly nonlinear equations. Burgers equation; Riemann problem

- Lecture 6 - Roe Solver for Burgers equation. Genereal relativity and hydridynamics; primitive and conserved variables

- Lecture 7 - Magneto-hydrodynamics in general relativity

- Lecture 8 - Magneto-hydrodynamics in general relativity (numerical implementation)

- Lecture 9 - Evolution in Maxwell equations

- Lecture 10 - Gravitational waves overview (nature in GR plus sources)

- Lecture 11 - Einstein's equation with generalized harmonic gauge conditions

- Lecture 12 - Gravitational waves

- Lecture 13 - BSSN/Generalized harmonic evolution

- Lecture 14 -Adaptive mesh refinement/parallel computation

### Explorations in Condensed Matter - Dmitry Abanin[edit | edit source]

- Lecture 1 - What is mesoscopics? Examples of mesoscopic systems

- Lecture 2 - Localization of electrons by disorder; week and strong localization; the concept of dephasing

- Lecture 3 - Scattering matrix approach to quantum transport; Landauer mechanism and localization

- Lecture 4 - Physical realization of !D transort; Band structure of graphene; Berry phases

- Lecture 5 - Integer Quantum Hall Effect (IQHE)

- Lecture 6 - Semiclassical percolation picture of Quantum Hall transition; Laughlin approach to transverse conductivity

- Lecture 7 - Hall conductivity and Berry phases; Hall conductivity as a topological invariant

- Lecture 9 - Fractional Quantum Hall effect and wave functions