PSI Lectures/2014

2013 <<<     >>> 2015

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

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&gt;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.

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