IISc Bangalore Course , Prof. Apoorva D Patel

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IISc Bangalore Course , Prof. Apoorva D Patel

KLEIN-GORDON AND DIRAC EQUATIONS:Introduction, The Klein-Gordon equation - Particles and antiparticles, Two component framework - Coupling to electromagnetism, Solution of the Coulomb problem - Bohr-Sommerfeld semiclassical solution of the Coulomb problem, The Dirac equation and the Clifford algebra - Dirac matrices, Covariant form of the Dirac equation, Equations of motion, Spin, Free particle solutions - Electromagnetic interactions, Gyromagnetic ratio - The Hydrogen atom problem, Symmetries, Parity, Separation of variables - The Frobenius method solution, Energy levels and wavefunctions - Non-relativistic reduction, The Foldy-Wouthuysen transformation - Interpretation of relativistic corrections, Reflection from a potential barrier - The Klein paradox, Pair creation process and examples - Zitterbewegung, Hole theory and antiparticles - Charge conjugation symmetry, Chirality, Projection operators, The Weyl equation - Weyl and Majorana representations of the Dirac equation, Unitary and antiunitary symmetries - Time reversal symmetry, The PCT invariance - Arrow of time and particle-antiparticle asymmetry, Band theory for graphene - Dirac equation structure of low energy graphene states, Relativistic signatures in graphene properties;LORENTZ AND POINCARE GROUPS:Groups and symmetries, The Lorentz and Poincare groups - Group representations, generators and algebra, Translations, rotations and boosts - The spinor representation of SL(2,C), The spin-statistics theorem - Finite dimensional representations of the Lorentz group, Euclidean and Galilean groups - Classification of one particle states, The little group, Mass, spin and helicity - Massive and massless one particle states - P and T transformations, Lorentz covariance of spinors - Lorentz group classification of Dirac operators, Orthogonality and completeness of Dirac spinors, Projection operators

QUANTUM ELECTRODYNAMICS:Propagator theory, Non-relativistic case and causality - Relativistic case, Particle and antiparticle contributions, Feynman prescription and the propagator - Interactions and formal perturbative theory, The S-matrix and Feynman diagrams - Trace theorems for products of Dirac matrices - Photons and the gauge symmetry - Abelian local gauge symmetry, The covariant derivative and invariants - Charge quantisation, Photon propagator, Current conservation and polarisations - Feynman rules for Quantum Electrodynamics, Nature of perturbative expansion - Dyson's analysis of the perturbation series, Singularities of the S-matrix, Elementary QED processes - The T-matrix, Coulomb scattering - Mott cross-section, Compton scattering - Klein-Nishina result for cross-section - Photon polarisation sums, Pair production through annihilation - Unpolarised and polarised cross-sections - Helicity properties, Bound state formation - Bound state decay, Non-relativistic potentials - Lagrangian formulation of QED, Divergences in Green's functions, Superficially divergent 1-loop diagrams and regularisation - Infrared divergences due to massless particles, Renormalisation and finite physical results - Symmetry constraints on Green's functions, Furry's theorem, Ward-Takahashi identity, Spontaneous breaking of gauge symmetry and superconductivity - Status of QED, Organisation of perturbative expansion, Precision tests

QUANTUM ELECTRODYNAMICS:Propagator theory, Non-relativistic case and causality - Relativistic case, Particle and antiparticle contributions, Feynman prescription and the propagator - Interactions and formal perturbative theory, The S-matrix and Feynman diagrams - Trace theorems for products of Dirac matrices - Photons and the gauge symmetry - Abelian local gauge symmetry, The covariant derivative and invariants - Charge quantisation, Photon propagator, Current conservation and polarisations - Feynman rules for Quantum Electrodynamics, Nature of perturbative expansion - Dyson's analysis of the perturbation series, Singularities of the S-matrix, Elementary QED processes - The T-matrix, Coulomb scattering - Mott cross-section, Compton scattering - Klein-Nishina result for cross-section - Photon polarisation sums, Pair production through annihilation - Unpolarised and polarised cross-sections - Helicity properties, Bound state formation - Bound state decay, Non-relativistic potentials - Lagrangian formulation of QED, Divergences in Green's functions, Superficially divergent 1-loop diagrams and regularisation - Infrared divergences due to massless particles, Renormalisation and finite physical results - Symmetry constraints on Green's functions, Furry's theorem, Ward-Takahashi identity, Spontaneous breaking of gauge symmetry and superconductivity - Status of QED, Organisation of perturbative expansion, Precision tests

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Relativistic Quantum Mechanics by Prof. Apoorva D Patel,Department of Physics,IISc Bangalore.For more details on NPTEL visit httpnptel.ac.in

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- 1.Introduction, The Klein-Gordon equation
- 2.Particles and antiparticles, Two component framework
- 3.Coupling to electromagnetism, Solution of the Coulomb problem
- 4.Bohr-Sommerfeld semiclassical solution of the Coulomb problem
- 5.Dirac matrices, Covariant form of the Dirac equation
- 6.Electromagnetic interactions, Gyromagnetic ratio
- 7.The Hydrogen atom problem, Symmetries, Parity, Separation of variables
- 8.The Frobenius method solution, Energy levels and wavefunctions
- 9.Non-relativistic reduction, The Foldy-Wouthuysen transformation
- 10.Interpretation of relativistic corrections, Reflection from a potential barrier
- 11.The Klein paradox, Pair creation process and examples
- 12.Zitterbewegung, Hole theory and antiparticles
- 13.Charge conjugation symmetry, Chirality, Projection operators
- 14.Weyl and Majorana representations of the Dirac equation
- 15.Time reversal symmetry, The PCT invariance
- 16.Arrow of time and particle-antiparticle asymmetry, Band theory for graphene
- 17.Dirac equation structure of low energy graphene states,
- 18.Groups and symmetries, The Lorentz and Poincare groups
- 19.Group representations, generators and algebra, Translations, rotations and boosts
- 20.The spinor representation of SL(2,C), The spin-statistics theorem
- 21.Finite dimensional representations of the Lorentz group, Euclidean and Galilean groups
- 22.Classification of one particle states, The little group, Mass, spin and helicity
- 23.Massive and massless one particle states
- 24.P and T transformations, Lorentz covariance of spinors
- 25.Lorentz group classification of Dirac operators, Orthogonality
- 26.Propagator theory, Non-relativistic case and causality
- 27.Relativistic case, Particle and antiparticle contributions, Feynman prescription
- 28.Interactions and formal perturbative theory, The S-matrix and Feynman diagrams
- 29.Trace theorems for products of Dirac matrices
- 30.Photons and the gauge symmetry
- 31.Abelian local gauge symmetry, The covariant derivative and invariants
- 32.Charge quantisation, Photon propagator, Current conservation and polarisations
- 33.Feynman rules for Quantum Electrodynamics, Nature of perturbative expansion
- 34.Dysons analysis of the perturbation series, Singularities of the S-matrix
- 35.The T-matrix, Coulomb scattering
- 36.Mott cross-section, Compton scattering
- 37.Klein-Nishina result for cross-section
- 38.Photon polarisation sums, Pair production through annihilation
- 39.Unpolarised and polarised cross-sections
- 40.Helicity properties, Bound state formation
- 41.Bound state decay, Non-relativistic potentials
- 42.Lagrangian formulation of QED, Divergences in Greens functions
- 43.Infrared divergences due to massless particles, Renormalisation
- 44.Symmetry constraints on Greens functions, Furrys theorem, Ward-Takahashi identity
- 45.Status of QED, Organisation of perturbative expansion, Precision tests

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