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Apprentice Mode
10 Modules / ~100 pages
Wizard Mode
~25 Modules / ~400 pages

Advanced Quantum Theory
( 25 Modules )

Module #1
Introduction to Advanced Quantum Theory
Overview of the course, review of basic quantum mechanics, and importance of advanced quantum theory
Module #2
Mathematical Preliminaries
Review of relevant mathematical tools:linear algebra, differential equations, and group theory
Module #3
Quantum Operators and Algebras
Introduction to quantum operators, algebras, and their representations
Module #4
Symmetries in Quantum Mechanics
Symmetries, conservation laws, and Noethers theorem
Module #5
Quantum Field Theory:Introduction
Basic concepts of quantum field theory, including fields, particles, and interactions
Module #6
Free Fields and Greens Functions
Free fields, Greens functions, and their applications
Module #7
Interacting Fields and Feynman Diagrams
Interacting fields, Feynman diagrams, and perturbation theory
Module #8
Renormalization Group and Running Couplings
Introduction to renormalization group, running couplings, and asymptotic freedom
Module #9
Topological Quantum Field Theory
Introduction to topological quantum field theory, topological invariants, and applications
Module #10
Integrable Systems and Quantum Inverse Scattering
Introduction to integrable systems, quantum inverse scattering, and Bethe ansatz
Module #11
Black Holes and Quantum Gravity
Introduction to black holes, event horizons, and quantum gravity
Module #12
Quantum Information and Entanglement
Introduction to quantum information, entanglement, and quantum computing
Module #13
Quantum Error Correction and Fault Tolerance
Quantum error correction, fault tolerance, and quantum error correction codes
Module #14
Many-Body Localization and Quantum Chaos
Introduction to many-body localization, quantum chaos, and ergodicity
Module #15
Superconductivity and Superfluidity
Introduction to superconductivity, superfluidity, and the BCS theory
Module #16
Quantum Phase Transitions and Criticality
Introduction to quantum phase transitions, criticality, and universality
Module #17
Nonequilibrium Quantum Systems
Introduction to nonequilibrium quantum systems, quantum transport, and dissipative dynamics
Module #18
Quantum Thermodynamics and Resource Theory
Introduction to quantum thermodynamics, resource theory, and thermodynamic cost
Module #19
Topological Insulators and Superconductors
Introduction to topological insulators, topological superconductors, and their applications
Module #20
Quantum Field Theory in Higher Dimensions
Quantum field theory in higher dimensions, AdS/CFT correspondence, and holography
Module #21
Conformal Field Theory and Bootstrap
Introduction to conformal field theory, bootstrap, and their applications
Module #22
Numerical Methods in Quantum Field Theory
Introduction to numerical methods in quantum field theory, lattice gauge theory, and Monte Carlo simulations
Module #23
Applications of Advanced Quantum Theory
Applications of advanced quantum theory to condensed matter physics, particle physics, and cosmology
Module #24
Current Research and Open Problems
Overview of current research and open problems in advanced quantum theory
Module #25
Course Wrap-Up & Conclusion
Planning next steps in Advanced Quantum Theory career


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