IISc Bangalore Course , Prof. Apoorva D Patel

**44**students enrolled

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

Up Next

You can skip ad in

SKIP AD >

Advertisement

- 2x
- 1.5x
- 1x
- 0.5x
- 0.25x

EMBED LINK

COPY

DIRECT LINK

COPY

PRIVATE CONTENT

OK

Enter password to view

Please enter valid password!

- Play Pause
- Mute UnMute
- Fullscreen Normal
- @Your Company Title

0:00

3.4 (26 Ratings)

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

Heads up!

These lecture videos are delivered by IISc Bangalore, under the NPTEL program, lot of nptel video courses are available for learning online.
38%

23%

15%

23%

- 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

- FreeVideoLectures aim to help millions of students across the world acquire knowledge, gain good grades, get jobs, assist in getting promotions through quality learning material.

- You can write to us
- help@freevideolectures.com

2018 FreeVideoLectures. All rights reserved. FreeVideoLectures only promotes free course material from different sources, we are not endrosed by any university.