An Introduction to Euler-Heisenberg Effective Actions

Abstract

Relativity, quantum mechanics and gauge invariance are essential
foundations in our theoretical understanding of modern physics in terms of
quantum field theory. The Euler-Heisenberg effective action encodes the
low energy modifications to gauge dynamics induced by quantum fluctuations
and vacuum polarization. Such effective actions contain a wealth of
physical information concerning both perturbative processes, such as
scattering amplitudes, and also non-perturbative processes, such as
quantum tunnelling and particle production. The Euler-Heisenberg effective
action for quantum electrodynamics is the basic paradigm for such
descriptions in a wide range of other physical applications including
quantum chromodynamics, nuclear, atomic, condensed matter, and
gravitational physics, and even string theory.

After a general introduction and historical review, the course will
concentrate on pedagogical methods for evaluating effective actions in
gauge theories. I will introduce and discuss semiclassical methods,
derivative (gradient) expansions, Borel summation, functional
determinants, and zeta function regularization. These are all essential
conceptual and computational methods for anyone planning to work in
quantum field theory or theoretical particle physics. The course is
intended to be self-contained, but requires familiarity with relativistic
quantum mechanics.

Gerald Dunne

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Department of Physics
University of Connecticut