Lecture 1 - Linear Algebra: Vector spaces, basis, scalar product, linear operators, matrix representationsLecture 2 - Group theory: Finite groups (cyclic and permutation groups), rotational groupsLecture 3 - Group Theory contd: O(3) and SO(3), U(n) and SU(n), Lorentz and Poincare groupsLecture 4 - Tangent and cotangent space, vectors and tensors, Clifford algebras, Grassman algebras.Student Presentations
edit
Lecture 1 - Distributions: test functions, Dirac delta function, Derivatives of distributions, Multiplication of distributions by functionsLecture 2 - Solution Methods: Reduction of order, Variation of parameters, Power series method, WKB approximationLecture 3 - Orthogonal Functions - Sturm-Liouville theory, Parseval's theorem, Orthogonal polynomialsLecture 4 - Special Functions and Complex Variables: Gamma function, Stirling's approxximation, Saddle point method, Zeta functionLecture 1 - Gaussian integrals in one dimension; Multi-dimensional Gaussian integrals; Averages with Gaussian weightLecture 2 - Wick's theorem; Imaginary Gaussian integrals; Gaussian integrals with Grassmann variablesLecture 3 - Functionals; Functional derivatives, Euler-Lagrange equations; Lagrangian MechanicsLecture 4 - Noether's theorem; Euler-Lagrange equations for continuous systems; Energy-momentum tensor; Constrained variationsLecture 1 - Green's functions, BVP, Poisson's equation, Green's identities, Method of imagesLecture 2 - Fourier transform, diffusion equation, heat kernel, FT in quantum mechanicsLecture 3 - Maxwell's equation, Wave equation, Retarded Potentials, Feynman-Wheeler theoryLecture 4 - Functional integral, Propagator, Degrees of freedom in gauge theoriesLecture 1 - Basic models of condensed matter; thermodynamics of free electron gasLecture 2 - Second quantisation; thermodynamics of free boson gasLecture 3 - Crystal lattices and Bloch's theoremLecture 4 - Motion in a periodic potential; tightly bound electrons
Lecture 1 - Motivation: Special relativity vs Newtonian GravityLecture 2 - Equivalence Principle, Coordinate TransformationsLecture 3 - General Covariance, Geodesic Equation, TensorsLecture 4 - Tensor Algebra, Tensor Densities, Covariant DerivativeLecture 5 - Curvature Tensor and its Properties, Conditions for FlatnessLecture 6 - Geodesic Deviation, Einstein's EquationsLecture 7 - Solutions of Einstein's Equations: Schwarzschild MetricLecture 8 - Charged Black Hole (Reissner-Nordstrom solution); Rotating Black Hole (Kerr Solution)Lecture 9 - Experimental Tests of GR: Precession of Perihelion, Deflection of LightLecture 10 - Experimental Tests of GR: Precession of Perihelion, Deflection of LightLecture 11 - Lagrangian Formulation, Einstein-Hilbert actionLecture 12 - Coupling Gravity to Matter: Scalar Field, Maxwell FieldLecture 13 - Brans-Dicke Theory, Vierbein FormalismLecture 15 - Cosmology: Friedmann-Robertson-Walker MetricLecture 1 - Motivations and axioms of quantum theory.Lecture 2 - Axioms continued. Density matrix. The Schroedinger and the Heisenberg Pictures.Lecture 3 - The Von Neumann Equation. Composite and Entangled Systems.Lecture 4 - Subsystems and Partial Trace. Schmidt Decomposition. Von Neumann Entropy.Lecture 5 - Partial criteria for Entanglement. Positive Partial Transpose (PPT). Sequential Measurement and Collapse. Von Neumann model of a measurement.Lecture 6 - Abstract model of von Neumann measurement. Decoherence.Lecture 7 - Interpretational controversy surrounding the collapse of the wave function. EPR Paradox.Lecture 8 - Dirac's abstract formulation of quantum and classical mechanics in terms of the Poisson braket and the commutator.Lecture 9 - Bell's inequalities. CHSH inequality. Hidden variables.Lecture 10 - Final comments relating to Bell's theorem. Infinite dimensional Hilbert Spaces. Self-adjoint operators on infinitte dimensional Hilbert Spaces.Lecture 11 - Infinite dimensions continued. Markov processes and classical path integrals. The Feynman path integral.Lecture 12 - The Feynman path-integral continued. Open quantum systems. Kraus operators.Lecture 13 - The optical Bloch equations. NMR and the Bloch equations.Lecture 14 - The Rotating Wave Approximation. Continuos Models of Markovian Open Systems and Dynamics [The Lindblad Formalism].Lecture 15 - Concepts and Examples from Quantum Information. Quantum Circuts. factoring. Quantum Teleportation.Lecture 1 - Particles and Second Quantization, Bose CondensationLecture 3 - Part 1 Part 2 - Klein-Gordon field, Conservation Laws, Noether's Theorem Lecture 4 -Part 1 Part 2 - Quantization of Klein-Gordon field, Heisenberg Representation, Dirac's Equation Lecture 5 -Part 1 Part 2 - Spinors and Spin, Dirac Conjugation Lecture 6 - Part 1 Part 2 - Dirac Lagrangian, Solutions of Dirac Equation, Quantization, Weyl Fermions, Helicity Lecture 7 - Part 1 Part 2 - Electromagnetic Field: Gauge Symmetry, EM Waves, Quantization Lecture 8 - Part 1 Part 2 - Quantum Electrodynamics, Dimensional Analysis and Perturbation Theory Lecture 9 - Part 1 Part 2 - Idea of Renormalization, Green's Functions, Wick's Theorem Lecture 10 -Part 1 Part 2 - Feynman Propagator, Feynman Diagrams Lecture 11 - Part 1 Part 2 - Scattering Amplitudes, Perturbation Theory in QED Lecture 12 - Part 1 Part 2 - Scattering of Electrons, Coulomb Law from QED, Yukawa Interactions Lecture 14 -Part 1 Part 2 - Examples of QED Calculation, QFT: Summary Future Directions Lecture 1 - From Hubbard Model to Heisenberg Model: SuperexchangeLecture 2 - From Hubbard Model to Heisenberg Model: Brillouin-Wigner renormalizationLecture 4 - Spin coherent state path integralLecture 5 - Spin wave theory from spin coherent path integralLecture 6 - Field theory for quantum antiferromagnets; non-linear sigma-modelLecture 8 - Negative U Hubbard Model; particle-hole canonical transformationLecture 9 - x-xz model; superconducting charge density wave and supersolid phasesLecture 10 - Field operators and boson coherent statesLecture 11 - Persistent currents and flux quantizationLecture 12 - Meissner effect, statics of vortices, Magnus forceLecture 1 - Euclidean time, Path Integrals, Relation between Euclidean field theory and statistical mechanicsLecture 2 - Operators and correlation functions in the path integral formalism, quantization of the free scalar field using functional integralsLecture 3 - Free scalar field: Functional integration using spacetime discretization, Correlation functionsLecture 4 - Free scalar field propagator, Quantization of φ4 theoryLecture 5 - Structure of perturbative expansion, Effective actionLecture 7 - Kallen-Lehman spectral representation, Mass renormalization of φ4 theoryLecture 8 - Coupling constant renormalization of massless φ4 theoryLecture 10 - Grassman variables, Berezin calculus, Fermionic Path integralsLecture 12 - Yang-Mills action, Coupling to matter, Feynman rulesLecture 14 - Faddeev-Popov determinant, ghosts, Feynman rules, Yang-Mills beta functionLecture 15 - Wilsonian renormalization, Renormalization of non-abelian gauge theoryLecture 1 - Introduction to phase transitions, Spatial Correlation FunctionsLecture 2 - Correlations and susceptibility, Critical exponents, Mean Field Theory Landau theoryLecture 3 - Vector order parameters, Spatially varying fieldsLecture 4 - Spin-spin correlation function in MFT, Scaling Power lawsLecture 5 - Two-parameter scaling, relations among critical exponents, Kadanoff length scalingLecture 6 - Ginzburg criterion, Gaussian modelLecture 7 - Gaussian model: partition function, free energy, internal energy, specific heat, critical regionLecture 8 - The renormalization group idea> Block spin renormalization for the 1-d Ising ModelLecture 9 - Block spin renormalization in d>1Lecture 10 - General RG theory; flows in the space of many couplings, scaling variablesLecture 11 - The ε expansion; the Gaussian model and the uσ4 modelLecture 12 - RG flow for model uσ4 continued; Wilson-Fisher fixed pointLecture 13 - Exponents from the ε expansion; corrections to scaling
Lecture 1 - Phase spaces for decay widths and cross-sectionsLecture 2 - Differential cross-sections and invariant amplitude: e^-e^+ to mu^- mu^+. The standard model gauge group. The Higgs doubletLecture 3 - Spontaneous symmetry breaking and massive gauge bosonsLecture 4 - The particle content of the standard model. Yukawa couplings. The CKM matrix.Lecture 5 - Interactions of gauge bosons with fermions. Interactions of the Higgs boson with fermions. Muon decay.Lecture 6 - Muon decay continued. Renormalization of QED. Dimensional reguralization.Lecture 7 - Computation of counterterms in QEDLecture 8 - Beta function for the electromagnetic coupling constant. Renormalization of QCD. Asymptotic freedom.Lecture 9 - Applications of asymptotic freedom. Charmonium and bottomonium.Lecture 10 - Structure functions. Proton + proton to Z + X.Lecture 12 - Renormalization of bottom mass. Chiral Lagrangian.Lecture 13 - Chiral perturbation theory. Light meson masses.Lecture 14 - Decay of pi minus. Application of chiral perturbation theory: The atmospheric neutrino problem. Discrete symmetries.Lecture 15 - Discrete symmetries continued. The PSI song. CP violation in the Standard Model. The CKM matrix and the unitarity triangle.Lecture 1 - Review of Ralativity, Light cone coordinates, CompactificationLecture 2 - Orbifolds, Nonrelativistic sting, Relativistic point particleLecture 3 - Relativistic strings, Nambu-Goto actionLecture 4 - Boundary conditions: D-branes, Static gauge, String in rest, Transverse velocityLecture 5 - String parametrization, equations of classical motion and constraintsLecture 6 - Symmetries and conserved momentum and Lorentz charges. general gauges.Lecture 7 - Equations of motion for free open strings, light-cone solutions, Virasoro operators.Lecture 8 - Light cone fields, Point particle quantizationLecture 9 - Quantization of point particle in light cone gauge, Momentum and Lorentz generatorsLecture 11 - Quantization of an open string II: critical dimension, tachyon, Maxwell fieldLecture 12 - Quantization of a closed string; Virasoro operators, graviton, dilatonLecture 13 - Strings on R^1/Z_2 orbifold. Action for fermionic strings.Lecture 14 - Quantizing superstrings: NS and R sectors, Spacetime fermions.Lecture 15 - Overview of superstring theories, D-branesLecture 1 - What's the problem? The realist strategy. The quantum measurement problem.Lecture 2 - The operational strategy. Operationalism vs realism.Lecture 3 - The most general preparations. The most general measurements.Lecture 4 - The most general types of transformations.Lecture 5 - A framework for convex operational theories. Operational classical theory. Operational quantum theory. Real vs complex field.Lecture 6 - Recasting the òrthodox`interpretation as a realist model. Realism via hidden variables. Psi-ontic vs psi-epistemic modelsLecture 7 - Evidence in favour of psi-epistemic hidden variable models. Restricted Liouville mechanics. Restricted statistical theory of bits.Lecture 11 - Generalized notions of non-contextuality.Lecture 13 - The deBroglie-Bohm interpretation continued.Lecture 2 - Differential Forms, Exterior and Lie DerivativesLecture 3 - Lie Derivative contd, Killing vectors, Connections and Curvature, Cartan's Equations of StructureLecture 4 - Examples: Gravitational Wave Spacetime, Warped CompactificationLecture 5 - The physics of curvature: accelerations vs gravity, geodesics in SchwarzschildLecture 6 - Derivation of Black Hole solutions: Schwarzchild, (A)dS Black Holes, Euclidean Black Holes and Hawking TemperatureLecture 7 - Lagrangians, Einstein-Hilbert Action, Energy-Momentum Tensors, Energy ConditionsLecture 8 - Domain wall solution, Cosmic string solutionsLecture 9 - Jordan-Brans-Dicke modified gravity, Jordan Einstein framesLecture 11 - Gauss-Codazzi formalism, Geometry of submanifoldsLecture 12 - Applications of Gauss-Codazzi, Gibbons-Hawking term, Israel equationsLecture 14 - Cosmic Censorship, (In)Stability of Black HolesLecture 15 - Gravity and String Theory, D-Branes, properties of AdSLecture 1 - Einstein-Hilbert action, Einstein's theory in 3DLecture 2 - Tetrad formalism: vielbeins, spin correction, torsion and curLecture 3 - First-order formalism, Symmetries of 3D gravity actionLecture 4 - Hamiltonian analysis, Canonical variables for gravity, Totally constraint systemLecture 5 - Constraints, Gauge transformations and constraint algebraLecture 6 - Phase space of systems wuth gauge symmetry, Dirac observables, Parametrized particleLecture 7 - Quantization of parametrized particle ILecture 8 - Quantization of parametrized particle IILecture 10 - Holomonies, Fluxes and their Poisson algebraLecture 11 - Outline of Quantization, SU(2) gymnasticsLecture 12 - Hilbert Space for One Edge, Action of Fluxes, Lenght QuantizedLecture 13 - Solving the Gauss Constraint, IntertwinerLecture 1 - The notion of a quantum phase transition: ground state energy, phase diagram. Quantum Ising Model in 1D, dualityLecture 2 - Universality in critical phenomena and scalingLecture 4 - Exact spectrum of transverse Ising model and correlation functions.Lecture 5 - Quantum Information approach to Quantum Phase TransitionsLecture 6 - Quantum-coherent transport in 1D systems; point contacts; scattering matrixLecture 7 - Electrons in disordered potential: Landauer formalism and perturbation theoryLecture 8 - Localization phenomena; scaling approach to localizationLecture 9 - Graphene: band structure, Dirac-like low energy excitationsLecture 10 - Graphene: conductivity and the role of disorderLecture 11 - Berry phases, Berry's curvature, examples.Lecture 12 - Integer Quantum Hall effect; edge states and the role of disorderLecture 13 - Quantum Hall effect: bulk and transition. Percollation and flux insertion approachesLecture 14 - Topological invariance and Hall conductivityLecture 1 - Lagrangian for complex scalar + Weyl fermion, Feynman rulesLecture 2 - 1-loop correction of fermion and scalar propagators, Hard cut-off regularization, LoLecture 3 - Dimensional regularization, Hierarchy problemLecture 4 - Technical naturalness, Canceling the quadratic divergence using supersymmetryLecture 5 - Supersymmetric gauge theory, Chiral supermultiplets, Vector supermultipletsLecture 6 - Supersymmetry transformations, Production of charginosLecture 7 - Dimensional analysis, Cross sections, Calculatin Feynman diagrams using Mathematica or MadGraphLecture 8 - Effective field theories in the Standard Model, Chiral Lagrangian, Fermi theoryLecture 9 - Effective field theories as probes of new physicsLecture 10 - The role of exact and approximate symmetries in new physics seachers. Approximate symmetries of the SMLecture 11 - Approximate symmetries of the SM continued. Parameter counting. CKM matrix.Lecture 12 - GIM mechanism, Kaon oscillations in the Standard Model, Kaon oscillations with supersymmetry, soft supersymmetry breakingLecture 1 - Qubits, unitary operators, superdense coding.Lecture 2 - Circuit models, reversible computation, universal gate sets.Lecture 3 - Implementations (non-linear optics).Lecture 5 - Computational complexity continued. Basic quantum algorithms: Deutsch-Jozsa.Lecture 6 - Phase estimation, quantum Fourier transform.Lecture 9 - Density matrices, quantum operations, POVMs.Lecture 10 - Distance measures, Helstrom measurementLecture 11 - Entropy, entanglement concentration, compressionLecture 12 - Quantum data compression continued. Quantum error correction.Lecture 1 - Review of Differential Geometry: Manifolds Tensors, the Connection, the MetricLecture 2 - Review of GR: Einstein equations, the Energy-momentum tensorLecture 3 - GR vs. Yang-Mills theory; Maximally symmetric space-timesLecture 5 - The FRW mwtric, Friedman equation, Continuity equationLecture 6 - Kinematics of FRW: geodesics, horizons; The horizon problemLecture 7 - The flatness problem; Matter, rediation and dark energy; the history of the UniverseLecture 8 - Thermodynamics Statistical Mechanics in the Universe; Decoupling and Freeze-outLecture 10 -Dark Matter: observational evidence candidatesLecture 11 - Cold Hot DM, non-thermal relics; BaryogenesisLecture 14 - QFT in curved space: Bogoliubov transformations, Unruh temperature
Lecture 1 - Neutron interferometry, pure state case.Lecture 2 - Uses of neutron interferometry, mixed state case.Lecture 3 - Incoherent processes in NI - magnetic field in one path.Lecture 4 - Incoherent processes in NI - wedge in one path.Lecture 7 - NMR. Rotating wave approximation.Lecture 8 - NMR. Bloch equations. Characterizing a qubit. Hahn echo.Lecture 2 - Dark Matter distributions. Thermal DM creationLecture 3 - Thermal creation of DM. The Boltzmann equation.Lecture 4 - DM freeze out. Justification of kinetic equilibrium. Solving the Boltzman equation. S-wave and p-wave. Yield.Lecture 5 - Computing yield from the Boltzmann equation. The WIMP miracle. Candidates for WIMPs: SupersymmetryLecture 6 - WIMPs continued. SUSY and R parity. Universal extra dimensions (UED). Resonant enhancement. Coannihilation.Lecture 7 - Coannihilation continued. Non-thermal DM. Gravitino as a DM candidate. Limitation of gravitino as a thermal DM candidate. SuperWIMP DM.Lecture 8 - Non-thermal DM: Massive particles decay. Asymmetric DM. Direct detection of DM. Kinematics of direct detection.Lecture 9 - Direct detection of DM. Scalar-Scalar interaction.Lecture 10 - Direct detection continued. Vector-vector and axial vector-axial vector interactions. Experimental searched for DM.Lecture 1 - Quantum systems; entanglement in bipartite systems; measures of entanglement Lecture 2 - Scaling of correlations and entanglement. Valence bond solids. Lecture 3 - Free fermions and computation of entropy for free fermions Lecture 4 - Ground states of quadratic Hamiltonians Lecture 5 - Entanglement and Universality Lecture 6 - Tensor network states; diagrammatic notation, propertiesm computational cost Lecture 7 - Matrix product states Lecture 8 - Transfer matrix and calculation of observables in MPS formalism Lecture 9 - Multi-scale entanglement renormalization ansatz (MERA) Lecture 10 - Projected entangled-pair states (PEPS) Lecture 11 - Quantum phases and symmetry breaking in many-body physics Lecture 12 - Fractional quantum Hall states and dancing picture of topological order Lecture 13 - String liquid: dancing rules and topological degeneracy of the ground state Lecture 14 - Definition of topological order; topological and local particle-like excitations Lecture 15 - Fractional statistics of topological quasiparticles Lecture 1 - Homogeneous universe, Penrose diagramsLecture 2 - Angular diameter distance, perturbed universe, gauge invariant perturbation theoryLecture 3 - Perturbed perfect fluid, Boltzmann equationsLecture 4 - First-order Boltzmann equation, collision termsLecture 5 - Large scale inhomogeneities during radiation domination, physical versus comoving scalesLecture 6 - Baryon acoustic oscillations, damping, Sachs-Wolfe effectLecture 7 - Power spectrum, acoustic oscillationsLecture 8 - Cosmic variance, Sachs-Wolfe pateau, comparing theory to Planck resultsLecture 11 - QFT in curved spacetime: particle productionLecture 12 - Correlation functions, Schroedinger picture for QFT, Bunch-Davies VacuumLecture 13 - Scalar fluctuations in an inflating backgroundLecture 15 - Comparing inflactionary models with Planck data, eternal inflationLecture 1 - Introduction to CFT's: MotivationLecture 2 - Definition of CFT's, Conformal transformationsLecture 3 - 2-point and 3-point correlation functions, CFT dataLecture 4 - State-operator correspondence, primaries descendants, unitary bounds, AdS spaceLecture 5 - Operator Product Expansion, Conformal blocksLecture 6 - Recent Advances in CFTs: Bootstrap EquationsLecture 8 - Open-Closed String Duality, Maldacena's Decoupling ArgumentLecture 9 - Maldacena's Decoupling Argument Part2: AdS/CFT CorrespondenceLecture 12 - Calculation of Anomalous Dimensions with Spin Chain TechniquesLecture 13 - Calculation of Anomalous Dimensions on the String Theory Side (Strong Coupling): the BMN and Folded String SolutionsLecture 14 - Spin Chains and Integrability; Bethe EquationsLecture 15 - Bootstrap Program: Integrable Model with O(4), Cusp Anomalous at All Couplings
