History 181B - Class 28

History 181B: Modern Physics

Class 28 (4/2/03)
Fields and particles (1)

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Outline

The quantum theory of fields
    QFT as a completion of quantum mechanics: Open problems
    QFT as a rational generalization of classical theory
    Quantizing new sorts of variables: Creation and annihilation operators
    Creating and destroying matter?
    Antiparticles, antimatter
        What these mean physically
        Thinking with a visual language
        Consequences for the vacuum
    What QFT delivers
    "Second" quantization and fields without classical counterparts

What are QFTs good for
    Quantum electrodynamics: Dirac (1927), Heisenberg-Pauli (1929-30)
        Recovering Maxwellian electrodynamics
        Reconstructing force as exchange of particles
    QED as a model for other QFTs
    The cloud on the horizon: QED's infinities

Names and terms

Primary	Secondary
photon = light quantum creation operator a* annihilation operator a antielectron = positron (e-bar) hole spontaneous pair creation energy-time uncertainty relation: delta E delta t >= h-bar/2 vacuum polarization effective charge quantum electrodynamics (QED) fine structure constant alpha = e² / h-bar c	number operator a *a virtual particle

Assignment

Paul A.M. Dirac, "Theory of Electrons and Positrons" (1933), in Nobel Lectures: Physics, 1922-1941 (Amsterdam: Elsevier, 1965), 320-325.

    After quantum mechanics, what did Dirac think was the next step for quantum theory?
    How did he connect the theory of elementary particles to relativity?
    How did he interpret the negative-energy solutions that came out of his equations? What were the positrons to which he connected them? What did he mean by a hole?
    How seriously would you have been inclined to take this theory if positrons had not yet been found experimentally?
    Extra: Look at the steps by which Dirac sets up his wave equation (3).