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Introduction to path integrals and interferometry.
Relationship of quantum theory to special relativity. The no-signalling principle.
Mixed states, entanglement, Bell's theorem and Bell experiments. Introduction to quantum
information and some applications.
Special relativity, foundations of general relativity, Riemannian geometry, Einstein's equations, FRW and Schwarzschild geometries and their properties.
Canonical quantization of fields, perturbation theory, derivation of Feynman diagrams, applications in particle and condensed matter theory, renormalization in φ4.
A brief review of ensembles and quantum gases, Ising model, Landau theory of phase transitions, order parameters, topology, classical solutions.
Feynman Path Integral, abelian and nonabelian gauge theories and their quantization, spontaneous symmetry breaking, nonperturbative techniques: lattice field theory, Wilsonian renormalization.
The general principles guiding the course will be broken symmetries, phases and emergent collective modes.
Part 1 - crystals: broken translational symmetry and phonons
Part 2 - magnets: broken spin rotational symmetry and magnons
Part 3 - normal metals, electronic properties
Part 4- superconductors: broken U(1) gauge symmetry, gaps and collective
This course will include the study of Perturbation Theory (Regular and Singular) Speeding Up Convergence and the Gibbs Phenomenon.
An introduction to the key ideas and techniques of CFT. These theories play a central role in the study of phase transitions in statistical physics and condensed matter systems, as well as in string theory.
Building on QFT 1 and 2, this course introduces nature's fundamental interactions and constituents as we understand them today. We will study effective field theory, the Lagrangian of the Standard Model, the symmetry patterns in mesons and baryons, spontaneous symmetry breaking, the Higgs mechanism (including recent LHC results), flavour physics, and open questions.
This class will cover the following topics: Phase Transitions, Order Parameters, Kosterlitz and Thouless phase transitions, Quantum Phase Transitions, Quantum XY model, Entanglement, Fidelity and Berry Phases in QPTs, Lattice Gauge Theories, Confinement-Deconfinement Transitions, Quantum and Topological Order, Toric Code and Topological Entropy.
Operational and realistic approaches to the interpretation of quantum mechanics. Local realism and the EDR argument. Bell's theorem and non-locality. Contextuality and the Kochen-Specker theorem. The deBroglie-Bohm interpretation. The many world interpretation.
Linear gravity and gravitons. Gravitational path integral. Perturbative Lorentzian quantum gravity (QG) and the need for non-perturbative QG. Constrained Hamiltonian systems. Canonical formulation of GR. Non-perturbative canonical QG. The Wheeler-De Witt equation. Loop QG. Non-perturbative path-integral for gravity: lattice and discrete methods (Regge calculus) and causal dynamical triangulations (CDT). Surprises in non-perturbative approach.
Relativist's toolkit: the geometric framework of GR, Cartan formalism, Gauss-Codazzi equations and Kaluza Klein theories. Black Holes: 4D solutions, black hole theorems, Hawking radiation and thermodynamics. Extra dimensions: simple supergravity solutions in string thoery (branes), the stability of these objects, then braneworlds and warped extra dimensions.
FRW metric, Hubble expansion, dark energy, dark matter, CMB. Thermodynamic history of the early universe. Growth of perturbations, CDM model of structure formation and comparison to observations, cosmic microwave background anisotropies, inflation and observational tests.
Basic concepts: qubits, quantim gates, quantim circuits, density matrices, quantum operations, entropy, entanglement. Topics in quantum algorithms and complexity: Languages, complexity classes, oracles, RSA, Deutsch-Jozsa algorithm, Shor's algorithm, Grover's algorithm. Information theory and implementations: Overview of implementations, quantum error correction, quantum cryptography, quantum information theory.
Why string theory? Bosonic string: massless fields in curved spacetime, point particle and Polyakov action, relativistic string, mode expansion, quantization, string spectrum, critical dimension, string theory as a theory of quantum gravity. Superstring: RNS formalism, spacetime fermions, critical dimension, type IIA and IIB superstring theories, 11D Supergravity and its dimensional reduction, D-branes, T-duality, U(N) gauge group from superstrings, M-theory, 5 string theories and their dualities.
Evidence and rational for physics beyond the Standard Model: Neutrinos, Baryogenesis, dark matter, scale hierarchies, electro-weak precision experiments; BSM physics: Supersymmetry (a tale of unification), Technicolor (superconductivity at the LHC), Extra-dimensions (Black holes, holography and strong coupling).
Theory and experiment of open quantum systems. Detailed look at selected physical realizations including: Neutron Interferometry (NI); NV centres in diamond; Superconducting qubits. In each of these cases: the mapping from physical system to qubit description; the physics of the system dynamics; the experimental state of the art; the limits of coherent control and quantum information processing.
QFT in curved space. Unruh effect. Inflation: homogenous limit, density perturbations, and CMBR. Vacuum decay in QFT. Quantum cosmology and the wavefuntion of the universe. False vacuum and stochastic eternal inflation. Challenges for inflation, alternatives to inflation.
Introduction to the AdS/CFT correspondence. Selected topics are presented on both sides of the gauge/gravity duality, using advanced field theoretical techniques. The decoupling argument and other motivation for the duality is given and the following topics are covered: Matrix models, Large N gauge theories, the 't Hooft limit, local and non-local observables (two and three-point functions, Wilson loops), the AdS space-time, minimal surfaces in AdS.
Introductory lectures on loop quantum gravity. Topics covered: Quanta of space, What is quatum gravity, Classical and quantum physics without time, classical GR in tertrad formalism, Holst action, Euclidean 3D gravity, Math of SU(2) and SL(2,C), Ponzanno-Regge transition amplitude, Kinematics of 4D Lorentzian quantum gravity, Spectrum of the volume operator, Coherent states, 4D partition function, Applications to cosmology and black hole physics.
A wide range of astrophysics observations suggest there is much more matter that what we can see. In this course we will outline the evidence for this dark matter, investigate some of the leading particle physics candidates for it, and discuss ways to study dark matter in the laboratory.
It will cover a variety of methods for solving the non-linear Einstein equations in the presence of matter in the curved space-time, as well as various problems of astrophysics in which strong non-Newtonian gravity plays a crucial role.
This course will be about the physics of mesoscopic devices such as two-dimensional electron systems, thin wires, point contacts, superconducting dots in which quantum effects in the motion of charge play the major roll.