PSI Lectures/2014

2013 <<<                      >>> 2015

Front

Complex Analysis - Tibra Ali

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

• Lecture 2 - Cauchy-Riemann equations. Holomorphic functions and harmonic functions. Cauchy's Theorem. Contour integration.

• Lecture 3 - Cauchy's integral theorem. Integral formula. Taylor and Laurent series. Singularities. Residue theorem

• Lecture 4 - Applications of the residue theorem. Semi-circular contours. Mouse hole contours. Keyhole integrals.

Quantum Mechanics - Agata Branczyk

• Lecture 1 - The wave function: c.f. with classical mechanics, statistical interpretation, normalization/Time-independent Schroedinger equation: paticle in a box, simple harmonic oscilator, free particle

• Lecture 2 - Schroedinger equation in 3D and the Hydrogen atom, Angular momentum, Spin, Addition of angular momentum

Lie Groups and Lie Algebras - Gang Xu

• Lecture 1 - Introduction: motivation, definition, examples, properties.

• Lecture 2 - Structure of a group: Representation of a group, structure constant, Poincare group

• Lecture 3 - Adjoint Representation, Highest weight method to construct representations of su(2)

• Lecture 4 - finding a su(2) subalgebra in a general simple Lie algebra, the root diagram of rank-2 Lie algebra, Dynkin diagram

Classical Mechanics - David Kubiznak

• Lecture 1 - Newtonian and Lagrangian mechanis, Noether's theorem

• Lecture 2 - Hamilton's equations, Poisson brackets, Canonical transformations

• Lecture 3 - Hamilton-Jacobi theory, Complete integrability

• Lecture 4 - Constraints, Nambu mechanics, Vibrations of string

Differential Geometry – Denis Dalidovich

• Lecture 1: Special relativity; Lorentz transformations; Tensors

• Lecture 2: Dual tensors; Metric job description; Gravity and Geometry

• Lecture 3: Covariant derivative, Riemann and Ricci tensors; Einstein equations

• Lecture 4: Important metrics, inflation, cosmological constant problem

Distributions and Special Functions – Dan Wohns

• Lecture 1: Distributions, Test functions, Derivatives of distributions

• Lecture 2: Multiplication of distributions with functions, Composition of distributions with functions, Functional derivatives, Gamma, Zeta

• Lecture 3: Orthogonal functions, Sturm-Liouville theory, Parseval's theorem, Orthogonal polynomials

• Lecture 4: Asymptotic series, Stirling's approximation, Saddle-point method

Green’s Functions – Denis Dalidovich

• Lecture 1: Green's functions for differential equations; self-adjoint differential operators. Sturm-Liouville problem and boundary conditions; eigenfunctions expansion.

• Lecture 2: Fourier transform and its properties. Causal Green's function. Partial Differential Equations (PDE's).

• Lecture 3: Heat (diffusion) equation and heat kernel. Laplace and Poisson equations, Green's function of Laplace operator.

• Lecture 4: Wave equation, Green's function for the wave equation. Maxwell's equations and retarded potentials

Core

Relativity - Neil Turok

• Lecture 1 - Maxwell's theory in relativistic notations.

• Lecture 2 - Lorentz transformations, time dilation, ruler contraction.

• Lecture 3 - Energy-Momentum tensor, the Lorentz Force, Noether Theorem.

• Lecture 4 - Action, Noether Theorem, Poincare group.

• Lecture 5 - Coupling to gravity, Riemann tensor.

• Lecture 6 - Geodesics for massive and massless particles, Affine parameterization.

• Lecture 7 - Weak field limit, gravitational shift, tensors and covariant derivative.

• Lecture 8 - The Riemann tensor, Einstein equations.

• Lecture 9 - The Einstein tensor, the deviation of geodesics, the Schwarzschild solution.

• Lecture 10 - The event horizon at the Schwarzschild radius, the tests of general relativity, the oribts of a massive particle.

• Lecture 11 - The perihelion shift, the Einstein-Hilbert action, the energy-momentum tensor. Lecture Notes

• Lecture 12 - The linearized gravity, The gravitaitonal waves part one.

• Lecture 13 - Gravitational waves part two.

• Lecture 14 - The interior of the Schwarzschild black hole.

• Lecture 15 - The Schwarzschild black hole in Kruskal coordinates, cosmology.

Quantum Theory - Joseph Emerson

• Lecture 1 - Motivations and introduction to axioms of quantum theory.

• Lecture 2 - The first two postulates of QM (Hilbert space and measurement)

• Lecture 3 - The second postulate continued; the third postulate of QM (transformations); Schroedinger and Heisenberg pictures

• Lecture 4 - Composite systems; properties of the tensor product; composite states and entanglement

• Lecture 5 - Practical postulates; density operators; Cholesky decomposition; reduced density operators partial trace; Generalized Postulate #1; Pure states vs Mixed states

• Lecture 6 - Generalized measurement; PVMs vs POVMs; measurement on composite systems; Generalized Postulate #2

• Lecture 7 - Generalized meas. cont.; Neumark Dilation Theorem; Trine "Mercedez-Benz" measurement; Projection postulate; von Neumann-Luders Rule

• Lecture 8 - Sequential meaurements, measurement as transformation, measruement as state preparation, significance of "collapse", disturbance, state-update rule for generalized measurement

• Lecture 9 - Guest lecture on quantum optics: quantization of the EM field; number (Fock) states; coherent states, cat states, Wigner functions

• Lecture 10

• Lecture 11 - Generalized Transformations; CPTP maps; Stinesprint dilation theorem; Decoherence; Amplitude damping channel;

• Lecture 12 - Vote on topics; Entanglement Nonlocality; Bell's theorem; CHSH inequality

• Lecture 13 - Bell's theorem cont.; EPR; Quantum information; CHSH game, Entanglement; Schmidt decomposition; criterial for mixed state entanglement

• Lecture 14 - Schmidt decomp. cont.; purification of a mixed state; Contextuality; Peres-Mermin square; Kochen-Spekker theorem

• Lecture 15 - Poisson bracket formulation of classical and quantum mechanics; Infinite dimensional systems; Rigged Hilbert space; Von Neumann's approach

Quantum Field Theory I - Daniel Wohns, Tibra Ali

• Lecture 1 - Classical field theory

• Lecture 2 - Canonical Quantization of the Klein-Gordon Field

• Lecture 3 - LSZ Reduction Formula

• Lecture 4 - Interaction Picture and Wick's Theorem

• Lecture 5 - Feynman Diagrams and Scattering Amplitudes

• Lecture 6 - Cross Sections and Decay Rates

• Lecture 7 - Introduction to Loops

• Lecture 8 - Introduction to Spinors

• Lecture 9 - Lagrangians for Spinors. Properties of Solutions of the Dirac Equation.

• Lecture 10 - Quantization of Spinors.

• Lecture 11 - Yukawa Theory. Feynman rules for fermions

Conformal Field Theory - Jaume Gomis, Pedro Vieira, Freddy Cachazo

• Lecture 1 - The role of conformal field theories in physics

• Lecture 2 - Conformal transformations, conformal algebra, embedding formalism

• Lecture 3 - (Gomis) AdS/CFT appetizer, role of the stress tensor in a CFT, restrictions of conformal invariance on correlators of local operators

• Lecture 4 - (Gomis) The Weyl anomaly in various dimensions, and irreversibility of the RG flow

• Lecture 5 - (Gomis) Entanglement entropy and sphere partition functions, radial quantization and the state-operator map, unitarity bounds

• Lecture 6 - (Vieira) Conformal invariance in D>2, consequences for correlators, state-operator map, conformal blocks, conformal bootstrap

• Lecture 7 - (Vieira) Casimir equation for conformal blocks, OPE in the free scalar theory

• Lecture 8 - (Vieira) A toy model of AdS/CFT: two- and three-point functions

• Lecture 9 - (Vieira) Conformal bootstrap, 2D and 3D Ising CFT

Statistical Mechanics - Anton Burkov

• Lecture 1 - Introduction to phase transitions, Ising model, Mean field theory

• Lecture 2 - Critical exponents α, β, γ, δ in MFT, Universality classes

• Lecture 3 - Hubbard-Stratonovich transformation, Spin-spin correlation function

• Lecture 4 - Correlation length in MFT, Lattice Fourier transform

• Lecture 5 - Beyond MFT: fluctuations, Upper critical dimension, Ginsburg criterion

• Lecture 6 - Landau-Ginsburg theory, Renormalization 1: fast and slow modes

• Lecture 7 - Renormalization 2: Integration over fast modes, Wave function renormalization, Fixed points

• Lecture 8 - Renormalization 3: RG recursion relations, 2nd cummulant-Feynman diagrams

• Lecture 9 - Renormalization 4: Gaussian and Wilson-Fisher fixed point, (Ir)relevant couplings

• Lecture 10 - Climax of renormalization: Critical exponents, Heisenberg model

• Lecture 11 - Goldstone modes, Lower critical dimension: Mermin-Wagner theorem, Non-linear Sigma model

• Lecture 12 - Vortices in d=2, Kosterlitz-Thoulers phase transition

• Lecture 13 - From d-dimensional quantum Ising model to (d+1)-dimensional classical one

• Lecture 14 - System response functions, Breakdown of quasiparticle description at a critical point

Quantum Field Theory II – Francois David

• Lecture 1: Path integral for a non-relativistic particle, Euclidean time

• Lecture 2: Operators and correlation functions in the path integral formalism, Thermal expectation values, Free scalar field

• Lecture 3: Propagator of the free scalar field, Correlation functions and Wick's Theorem

• Lecture 4: Quantization of φ4 theory, Feynman rules, Cancelation of vacuum diagrams

• Lecture 5: Structure of perturbation theory, Generating functionals, Effective action at one loop

• Lecture 6: Effective action at one loop continued, Mass renormalization in φ4 theory

• Lecture 7: Renormalization of massless φ4 theory at one loop, Beta function

• Lecture 8: Renormalization of massive φ4 theory at one loop, Wilsonian renormalization

• Lecture 9: Renormalization group flow

• Lecture 10: Grassman variables and Berezin calculus, Fermionic path integrals

• Lecture 11: Non-abelian gauge theory

• Lecture 12: Coupling non-abelian gauge fields to matter, Gauge fixing

• Lecture 13: Quantization of non-abelian gauge theory, Faddeev-Popov determinant, Ghosts, Feynman rules

• Lecture 14: Renormalization of non-abelian gauge theory

• Lecture 15: Higgs Mechanism

Condensed Matter – Marcel Franz

• Lecture 1: Solids as interacting quantum many-body systems, basic Hamiltonian. Born-Oppenheimer approximation.

• Lecture 2: Second quantization for fermions and bosons

• Lecture 3: Electron gas; jellium model; ground state energy due to interactions.

• Lecture 4: Hartree-Fock (mean-field) approximation. Screening: Thomas-Fermi (semiclassical) approximation, Lindhard dielectric function.

• Lecture 5: Bose-Einstein condensation; Bogoliubov theory of liquid helium: Hamiltonian, Bogoliubov transformation, energy spectrum

• Lecture 6: Lattice vibrations, phonons; Phonon specific heat and the Debye model.

• Lecture 7: Magnons, Heisenberg Hamiltonian, Holstein-Primakoff transformation, ferromagnetism.

• Lecture 8: Electrons in a periodic potential, Bloch's theorem, the case of weak potential.

• Lecture 9: Band structures, metals, insulators. Tight-binding Hamiltonians.

• Lecture 10: Transport: Semiclassical theory of electron dynamics, relaxation time approximation.

• Lecture 11: Topological phases of matter: examples, band theory,Berry curvature and phase. Polarization and topology.

• Lecture 12: Polyacetylene and the Su-Schrieffer-Heeger model; Chern insulator; Energy spectrum of graphene and time-reversal invariance.

• Lecture 13: Hamiltonian for graphene and inversion symmetry; Haldane and Semenoff masses. Superconductivity: Cooper pair problem.

• Lecture 14: Electron-phonon coupling and attractive interaction; BCS ground state, gap equation and its solution at zero temperature.

• Lecture 15: Bogoliubov-deGennes theory of superconductivity; BCS gap at finite temperature; Ginzburg-Landau theory and electromagnetic properties.

Review

Foundations of Quantum Mechanics – Lucien Hardy

• Lecture 1 - Course outline, Interferometers, Elitzur-Vaidman bomb tester (paper)

• Lecture 2 - Axioms of QM, The reality problem (a.k.a. The measurement problem), No-cloning theorem (paper)

• Lecture 3 - Decoherence-induced prefered basis, Quantum Zeno effect (link to paper), Quantum-optical interferometry

• Lecture 4 - Einstein's comments at Solvay 1927 (pdf), Einsteing-Podolsky-Rosen paradox (paper), Harrigan-Spekkens classification scheme (pdf)

• Lecture 5 - de Broglie-Bohm theory (pdf)

• Lecture 6 - Measurement in de-Broglie Bohm

• Lecture 7 - Many Worlds interpretation

• Lecture 8 - Issues with Many Worlds, Collapse models (pdf)

• Lecture 9 - GRW Bell collapse model (jumps)

• Lecture 10 - Ontological excess baggage theorem, Spekken's toy model (pdf)

• Lecture 11 - Contextuality

• Lecture 12 - Generalized Probability Theories

Standard Model – Gordan Krnjaic and Stefania Gori

• Lecture 1 - Introduction and Cast of Characters

• Lecture 2 - Two-component spinors

• Lecture 3 - Goldstone Theorem and Higgs Mechanism

• Lecture 4 - Electroweak Symmetry Breaking

• Lecture 5 - Electroweak Symmetry Breaking Continued, Leptons

• Lecture 6 - Lepton Masses, Feynman Rules

• Lecture 7 - Electroweak Interactions of Quarks

• Lecture 8 - CKM Matrix

• Lecture 9 - Introduction to Renormalization

• Lecture 10 - Renormalization of QED

• Lecture 11 - Renormalization of QED continued, Introduction to QCD

• Lecture 12 - QCD Feynman Rules, QCD Beta Function, Introduction to Kaon Oscillations

• Lecture 13 - Kaon Oscillations, GIM Mechanism

• Lecture 14 - Neutrino Oscillations

• Lecture 15 - Neutrino Oscillations, Neutrinoless Double Beta Decay, Hierarchy Problem

Gravitational Physics - Ruth Gregory

• Lecture 1 - Manifolds, tangent and cotangent bundles, coordinate transformations

• Lecture 2 - Differenitation on manifolds, exterior derivatives, differential forms, Hodge duality.

• Lecture 3 - Lie derivatives and covariant derivatives. Maps between manifolds.

• Lecture 4 - The Cartan formalism. Application to spherically symmetric spacetimes.

• Lecture 5 - Black holes. Chandrasekhar limit. Carter-Penrose diagrams. de Sitter and anti-de Sitter space-times. Temperature of Schwarzschild BH.

• Lecture 6 - Gravity and field theory. Action principles and area. Domain walls and gravity.

• Lecture 7 - Gauss-Codazzi formalism and the Gibbon-Hawking boundary term.

• Lecture 8 - Black hole theormodynamics. Kerr metric. Entropy using Euclidean quantum gravity.

• Lecture 9 - Geodesics and ISCOs in Kerr. Rindler, C-metric.

• Lecture 10 - Black branes, higher dimensional black holes and black rings.

• Lecture 11 - Kaluza-Klein theory

• Lecture 12 - Gravitational perturbation theory. The Gregory-Laflame instability of black strings.

• Lecture 13 - Warped compactifications. Rubakov-Shaposhnikov mechanism. Randall-Sudrum mechanism.

• Lecture 14 - Gravitational instantons. Coleman-De Luccia instanton and bubble nucleation via black holes. Interesting related article: http://arxiv.org/abs/1401.0017.

• Lecture 15 - Beyond Einstein gravity. Modifying gravity with scalars. Chameleons. Gravitatoinal waves detection experiments.

Condensed Matter Review - Alioscia Hamma

• Lecture 1 - The notions of aquantum phase, order, symmetry breaking. Evolution of quantum systems. The notion of a quantum phase transition, universality, dynamical ctitical exponent, types of phase transitions and level crossing.

• Lecture 2 - Local quantum systems. Quantum Ising Model and spontaneous symmetry breaking.

• Lecture 3 - Classical to Quantum mapping. Transfer matrix method.

• Lecture 4 - The method of duality in the study of 1D quantum Ising model. Fidelity between the states

• Lecture 5 - Geometry of quantum phases and quantum phase transitions

• Lecture 6 - Locality in quantum many-body physics; Lieb-Robinson bounds

• Lecture 7 - Applications of Lieb-Robinson bounds: no signaling, spreading of correlations. Lieb-Mattis-Schultz theorem. Spreading of entanglement.

• Lecture 8 - Lattice gauge theory. Elitzur's theorem. Quantum phase transitions without symmetry breaking

• Lecture 9 - Quantum Lattice Z_2 gauge theory: ground states

• Lecture 10 - Quantum Lattice Z_2 gauge theory: duality and phases. Toric code Hamiltonian.

• Lecture 11 - Toric code: string operators, emergent fermions. Topological order, entanglement

• Lecture 12 - Entanglement. Robust properties of topological order.

• Lecture 13 - Equilibration and thermalization in quantum mechanics.

• Lecture 14 - Closed system dynamics. Generalised Gibbs state.

Cosmology Review - Kurt Hinterbichler David Kubiznak

• Lecture 1 - Maximally symmetric spaces

• Lecture 2 - FRW spacetime and its kinematics: Hubble's law, cosmological redshift, horizons

• Lecture 3 - Dynamics of FRW: Friedmann equations, current cosmological model

• Lecture 4 - Thermodynamics in expanding Universe

• Lecture 5 - Brief thermal history, Big Bang Nucleosynthesis

• Lecture 6 - CMB Dark Matter

• Lecture 7 - Dark Matter Dark Energy

• Lecture 8 - CMB anisotropies: power spectrum observed and theoretical

• Lecture 9 - CMB polarization, Inflation: 3 puzzles

• Lecture 10 - Slow roll inflation, Fluctuations comoving horizon

• Lecture 11 - Quantizing time dependent harmonic oscillator

• Lecture 12 - Scale invariant power spectrum

• Lecture 13 - Calculation of inflationary power spectra 1

• Lecture 14 - Calculation of inflationary power spectra 2

• Lecture 15 - Surprise lecture

String Theory Review - Davide Gaiotto

• Lecture 1 - Motivation for string theory.

• Lecture 2 - The Nambu-Goto action and the Polyakov action.

• Lecture 3 - The stress-energy tensor and the Virasoro algebra.

• Lecture 4 - The string spectrum.

• Lecture 5 - BRST quantization part 1

• Lecture 6 - BRST quantization part 2

• Lecture 7 - State operator correspondence

• Lecture 8 - Vertex operator on a sphere, ghost vertex operator, 3-pt scattering amplitude

• Lecture 9 - The Virasoro-Shapiro amplitude

• Lecture 10 - The spacetime action for strings in curved spacetime, T-duality

• Lecture 11 - D-branes as sources of closed strings.

• Lecture 12 - D-branes and open strings.

• Lecture 13 - Super-particle world-line formalism.

Beyond the Standard Model - David Morrissey

• Lecture 1 - Motivation for Beyond the Standard Model physics

• Lecture 2 - Dimensional analysis and renormalization

• Lecture 3 - Non-renormalizable theories, symmetries, and effective theories

• Lecture 4 - Intro to supersymmetry

• Lecture 5 - Supermultiplets, superpotentials, supersymmetric actions, Wess-Zumino model, SUSY QED

• Lecture 6 - Soft SUSY breaking terms, MSSM, R-parity

• Lecture 7 - SUSY breaking in MSSM continued, spontaneous SUSY breaking

• Lecture 8 - Models of SUSY breaking, lightest superpartner as dark matter

• Lecture 9 - SUSY and fine-tuning, searching for SUSY at the LHC, QCD at low energies

• Lecture 10 - Chiral perturbation theory

• Lecture 11 - Technicolor, extended technicolor

• Lecture 12 - Composite and Little Higgs, extra dimensions

• Lecture 13 - Signals of extra dimensions, warped extra dimensions

• Lecture 14 - Gravitons and fermions from extra dimensions and connection to AdS/CFT.

Quantum Gravity - Bianca Dittrich

• Lecture 1 - Introduction to quantum gravity. Einstein-Hilbert action. Triads.

• Lecture 2 - Triads and connections. Action for 3D gravity.

• Lecture 3 - Global and local symmetries, Noether's theorem. Gauge symmetries in 3D first order gravity action.

• Lecture 4 - Canonical Analysis of the 3D First Order Action. Gravity Hamiltonian.

• Lecture 5 - Constraint algebra, phase space for gauge systems.

• Lecture 6 - (Dirac-) quantization of gauge systems.

• Lecture 7 - Quantum geometry. Holonomies.

• Lecture 8 - Fluxes, Holonomies and their Poisson algebra

• Lecture 9 - Quantization of Edges

• Lecture 10 - Length operator

• Lecture 11 - Quantization of triangles: solving the Gauss constraint

• Lecture 12 - Quantization of tetrahedra: solving the flatness constraint

• Lecture 13 - "Transition amplitudes" and creation of 3D Universe

• Lecture 14 - 4D LQG

Quantum Information - Daniel Gottesman

• Lecture 1 - Reversible computation, quantum gates

• Lecture 2 - Universal gate sets, no-cloning theorem, teleportation, distance between q. states (fidelity and trace distance)

• Lecture 3 - DiVincenzo Criteria, Ion traps

• Lecture 4 - Optical Quantum Computing

• Lecture 5 - Complexity theory, Church-Turing thesis,

• Lecture 6 - Oracle model, Deutsch-Josza algorithm

• Lecture 7 - Public key cryptography, RSA, period finding, overview of Shor's algorithm

• Lecture 8 - Shor's algorithm

• Lecture 9 - Grover's algorithm

• Lecture 10 - Error correcting codes

• Lecture 11 - Stabilizer codes, CSS codes, Fault tolerance

• Lecture 12 - Quantum Key Distribution

• Lecture 13 - Von Neumann entropy, Data compression, Quantum compression

• Lecture 14 - Quntum channel capacity, Entanglement monotones