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Quantum Field Theory. Note « 14 »
Exercises

  1. Bremsstrahlung -- radiation under deceleration (bremsestråling)

    Consider an interaction Lagrangian Lint=-gψγ5ψφ.
    1. Draw the lowest order diagram which describes bremsstrahlung of bosons in fermion-antifermion scattering.
    2. Identify all diagrams that give different contributions to the reaction amplitude and write down the corresponding contributions.
    3. Do the same for Lint=-gψγμψφAμ

  2. Particle oscillations

    Consider a Lagrangian
    L = 1/2∂μσ∂μσ + 1/2∂μπ∂μπ - 1/2M2 [cos(θ)σ + sin(θ)π]2 - 1/2m2 [-sin(θ)σ + cos(θ)π]2 ,
    where M≠m.
    1. What is the spectrum of particles?
    2. Suppose these particles interact with some fermions ψ with the interaction Lagrangian Lint=- gψψ(σ+π). Which of our particles is generated by this interaction, say, in the bremsstrahlung process, and how will it develop with time?
    3. Hint: Consider a state with one particle σ in the Schroedinger picture.

  3. Interaction with classical field

    Consider an interaction Lagrangian Lint=-gψγμψAμ. Suppose the the field Aμ is classical, that is a given function of time and coordinates.
    1. What is the lowest order scattering amplitude of a (nonrelativistic) fermion in this classical field?
    2. What is the lowest order correction to the energy of a (nonrelativistic) fermion in a static electric field?
    3. What is the lowest order correction to the energy of a (nonrelativistic) fermion in a static magnetic field?
    4. What is the magnetic moment of the fermion?
    5. Draw the digram that represents the lowest order correction to the magnetic moment of the fermion (anomalous magnetic moment).
    6. Calculate it :). (Schwinger, Nobel prize).
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