Course11510800160 lectures
Quantum Field Theory and Quantum Entanglement
Prof. Sudhir K Vempati · IISc Bangalore
About
This is a first course on Quantum Field Theory with Entanglement in view. Quantum field theory is one of the most important developments of the previous century. It provides a framework to understand the kinematics and the dynamics of relativistic particles in the quantum regime. The present takes off from the place where the course on quantum mechanics in the relativistic regime finishes. It starts with review of classical field theory and then go on to study quantisation conditions for scalar, Dirac and electromagnetic field theories. At the same time, it also aims to introduce modern concepts of entanglement in quantum field theory. It will introduce the first set of quantities required for entanglement – density matrices, spin correlators etc. Then we introduce entanglement in scattering processes and then we show to how entanglement appears in QED scattering processes.
Intended audience: Masters Students and Ph. D students
Prerequisites: MSC in physics courses: quantum mechanics, special theory of relativity, electrodynamics, relativistic quantum mechanics (preferable).
Lectures
Week 1 Introduction to Scalar Fields and Quantization
- Introduction and Overview
- Quantization in Quantum Mechanics
- Scalar Field Theory
- Quantization of Scalar Field Theory - I
- Quantization of Scalar Field Theory – II
Week 2 Scalar Field Quantization and Interactions
- Vacuum of scalar quantum fields
- Particle interpretation of scalar fields
- Quantisation of complex scalar field
- Introduction to interactions in Quantum field theories
- Interaction in quantum field theories
Week 3 Scattering processes in QFT
Week 4 Free Dirac Theory
- Dirac Spinors
- Properties of Dirac Spinors
- Dirac Equation
- Solutions of Dirac Equation
- Discrete Symmetries
Week 5 Fermion Quantization
- Plain Wave Solutions of DE
- Shortcomings of bosonic quantization of spinors
- Quantizing the Dirac Field
- Fermionic Propagators
- Feynman Rules for fermions
Week 6 Quantising the Electromagnetic Field
- Yukawa Theory
- Interactions of bilinears
- Quantising EM field
- Coulomb gauge quantisation
- Lorenz gauge quantisation
Week 7 Quantum Electrodynamics
Week 8 Regularization of QED
- Radiative corrections
- Renormalizability of QED
- Superficial degree of divergence
- Regularization schemes
- Dimensional Regularization of QED
Week 9 Renormalization of QED
- Electron Self-Energy
- Vacuum Polarization I
- Vacuum Polarization II
- Vertex Function I
- Vertex Function II
Week 10 Introduction to Quantum entanglement
- Einstein-Podolsky-Rosen (EPR) Paradox
- States in the product space
- Properties of product states
- EPR Paradox revisited
- Density operator/matrix
Week 11 Bell states, Correlations and Inequalities
- Matrix SVD and the Bell Basis Formalism
- Bell States and Correlations
- EPR like Experiments Continued
- Bell States and Inequalities
- Bell And CHSH Inequalities
Week 12 Entanglement in Quantum Field Theories
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IISc Bangalore
- Department
- Physics
- Teacher
- Prof. Sudhir K Vempati
- Level
- Graduate
- Language
- English
- Subjects
- Physics
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
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