Important Feynman Diagrams

Feynman diagrams are visual tools in Quantum Field Theory that simplify complex particle interactions. They help us understand processes like electron-positron annihilation, Compton scattering, and pair production, revealing the underlying principles of particle behavior and energy conservation.

1. Electron-positron annihilation

   • Occurs when an electron and a positron collide, resulting in the production of photons.
   • The process can produce one or more photons, typically two in the simplest case.
   • Important for understanding particle-antiparticle interactions and conservation laws (energy, momentum).
   • Feynman diagrams illustrate the interaction as a vertex where the electron and positron annihilate.

2. Compton scattering

   • Involves the scattering of a photon off a charged particle, usually an electron.
   • Demonstrates the particle-like behavior of light and the concept of momentum transfer.
   • Key for understanding the interaction between light and matter, particularly in quantum electrodynamics (QED).
   • Feynman diagrams show the photon interacting with the electron, resulting in a change in the photon’s energy and direction.

3. Pair production

   • Refers to the creation of a particle-antiparticle pair (e.g., electron and positron) from a high-energy photon.
   • Requires sufficient energy to satisfy the mass-energy equivalence principle (E=mc²).
   • Important for understanding the conversion of energy into matter and the role of virtual particles.
   • Feynman diagrams depict the photon interacting with a nucleus or another photon to produce the pair.

4. Electron self-energy

   • Describes the correction to the mass and charge of an electron due to its interactions with virtual photons.
   • Illustrates the concept of renormalization in quantum field theory, where infinities are managed.
   • Essential for accurate predictions of electron behavior in quantum electrodynamics.
   • Feynman diagrams show loops where the electron emits and reabsorbs virtual photons.

5. Vacuum polarization

   • Refers to the phenomenon where a photon temporarily creates virtual particle-antiparticle pairs in a vacuum.
   • Affects the effective charge of particles and modifies the propagation of photons in a vacuum.
   • Important for understanding the behavior of electromagnetic interactions at quantum levels.
   • Feynman diagrams illustrate the photon interacting with a virtual pair, leading to a modification of its properties.

6. Vertex correction

   • Involves the modification of the interaction vertex in Feynman diagrams due to quantum corrections.
   • Accounts for the effects of virtual particles on the strength of interactions between charged particles.
   • Crucial for precise calculations in quantum electrodynamics and other quantum field theories.
   • Feynman diagrams depict additional loops at the vertex where particles interact.

7. Bhabha scattering

   • Describes the scattering process between two electrons or two positrons, including both annihilation and pair production.
   • Important for studying electron-positron interactions and testing quantum electrodynamics.
   • Provides insights into cross-section calculations and the behavior of charged particles.
   • Feynman diagrams illustrate the various possible interactions and outcomes of the scattering process.

8. Møller scattering

   • Involves the scattering of two electrons, highlighting the effects of electromagnetic interactions.
   • Important for understanding electron-electron interactions and the role of virtual photons.
   • Provides a framework for studying scattering processes in quantum electrodynamics.
   • Feynman diagrams depict the exchange of virtual photons between the two electrons.

9. Photon propagator

   • Represents the mathematical description of how photons propagate through space-time in quantum field theory.
   • Essential for calculating scattering amplitudes and understanding interactions involving photons.
   • The propagator accounts for the effects of virtual particles in the interaction processes.
   • Feynman diagrams utilize the photon propagator to connect vertices in interactions.

10. Fermion propagator

    • Describes the propagation of fermions (e.g., electrons) in quantum field theory.
    • Key for calculating the behavior of fermionic particles in interactions and scattering processes.
    • The propagator incorporates the effects of virtual particles and the mass of the fermion.
    • Feynman diagrams use the fermion propagator to connect interactions involving fermions.