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Quantum Electrodynamics

Quantum Electrodynamics. Dirac Equation : spin 1/2. Feynmann Diagrams. Moller Scattering. Interaction is mediated by exchange of a  photon. Bhaba Scattering. electron positron annhilation. Symmetries, Groups and Conservation laws.

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Quantum Electrodynamics

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  1. Quantum Electrodynamics Dirac Equation : spin 1/2

  2. Feynmann Diagrams

  3. Moller Scattering Interaction is mediated by exchange of a  photon Bhaba Scattering electron positron annhilation

  4. Symmetries, Groups and Conservation laws Closure: R1,R2 belong to G, R1.R2 also belongs to G Identity: There exists element I such that for all elements in G IRi=RiI=Ri Inverse: For every element there exists an inverse element such that RiRi-1=I Associativity:

  5. Symmetries and Conservation Laws Noether's theorem: Every continuous symmetry implies a corresponding conservation law and conversely, every conservation law reveals a symmetry in the system. Rotation ---- Angular momentum Time translation ----- Energy

  6. SU(2) Symmetry Group: Isospin • mass of proton ~ mass of neutron • treating proton as a different charge substrate of neutron: Isospin (I) I=1/2. (conserved in strong interactions) • I3  =+/- 1/2 -----> charge Q/e=1/2+ I3   • Analogous to a particle of  ordinary spin 1/2 Generators of SU(2) are Pauli matrices:

  7. SU (3) symmetry: Flavour symmetry Generators of SU(3):Gell Mann Matrices

  8. Charge Conjugation: C Particle to antiparticle Parity Operation: P, reflects a system through the origin right handed system to left handed system axial system invariant under parity C and P are conserved in EM and Strong Interactions Time Reversal: T . Changes the direction of motion CPT invariance: All interactions are invariant under combined C,P,T

  9. Weak Interactions • All  quarks, leptons carry "weak charge"  • Short range interaction • Interact via exchange of W+,W- and Z bosons (massive) • two kinds of weak interactions: charged (W bosons) and neutral (Z boson) • Examples :decay processes

  10. Weak Interactions: Leptons charged neutral

  11. Conservation of electron, muon, tau numbers

  12. Conservation laws in WI • Conservation of charge • Conservation of Colour • Conservation of Baryon number • Electron, muon, tau number

  13. CP violation in Weak Interaction Weak Interactions are not always CP invariant. CP violation implies Time reversal must also be violated.

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